Using Fresnel lenses for
Because of their low cost, low weight and availability in large
sizes, Fresnel lenses are attractive options when used for
optical communications. Being generally equivalent to PCX
they can be used for collimating beams of light as well as
intercepting and focusing light from a distant source onto an
Because such use isn't really what the designers of the Fresnel
lenses had in mind, the question comes arises as to how "good"
they are for such purposes? This is what we hope that this
page at least partially answers.
What's a Fresnel lens?
Figure 1: Comparison
of a Fresnel lens (left) and a "conventional" plano-convex
lens (right). As can be seen, the Fresnel lens
simulates the shape of the conventional lens using
individual "facets" (also referred to "ridges" or
"grooves") - each of which contain a portion of the lens's
overall figure. The grooves of the lenses described
on this page face "outwards", away from the focal plane.
Authorship details of this public-domain image
may be found here.
By the late 1700's lens making was a well-established art, but
it occurred to some that most of the glass in the lens was
superfluous: For some applications - such as the directing
of beams of light - maintaining image quality was not important,
but the use of a "conventional" lens simply wasn't practical
owing to considerations of weight, cost, and ease of
At around 1818 Augustin-Jean Fresnel
used this realization to construct what is believed to be the
first practical version of such a lens and it found immediate
use in lighthouses
owing to its ability to effectively collect and concentrate a
significant portion of the lamp's overall light output and
direct it as a tight beam. By being able to simultaneously
collect much of the "wasted" light from the flame being emitted
in other directions while minimizing the divergence of the
resulting beam, this "Fresnel
" was able to increase the distance over which a
lighthouse's beam could be seen essentially to that of
As can be seen from Figure
the Fresnel Lens's primary advantage is that its weight
and thickness can be greatly reduced by utilizing only
those portions of the
lens that actually contribute to the "bending" of the light's
rays. In its original primary application - lighthouses -
the fact that the lens was broken up into smaller "facets" was of
little importance, even though such a lens wasn't particularly
useful for imaging purposes such as telescopes. What it is
good at is concentrating light (such as from the sun)
small area or at producing reasonably well-collimated
beams from light sources.
Fresnel lenses are typically made to be equivalent to an aspherical
lens - a property allows them to properly focus light with
- even with a small F-number
a very short focal length (hence, a small F-number)
lens/lamp assembly could be made to be reasonably small and
light - an important consideration if it was to be used in a
lighthouse and rotated about the source!
Another excellent reference on this topic is Fresnel
Technology's brochure, Fresnel
link to .PDF.
Limitations of Fresnel lenses
Even though lighthouses are relatively rare, Fresnel lenses are
now quite commonplace. Their main attraction is that they
can now be made rather inexpensively, the shape of the lens
being molded using plastic and can be found in products as
diverse as projection televisions, infrared
and photographic flash units. With modern
techniques it is now possible to shrink the size of the facets
such that even a large, "strong" lens can be made to be only a
few millimeters thick.
Despite modern manufacturing techniques and materials Fresnel
lenses are still inferior to "conventional" lenses when it comes
to being able to produce high-resolution images - and for
- Material stability. Being stamped into thin
material, it is important that it be kept flat.
Without much intrinsic strength, distortions, bowing and
warping are inevitable in lenses made from thin plastic.
- Precision. During manufacture, thermal
expansion/contraction of the plastic can complicate precise
replication. Slight variations of the mechanical and
optical properties of the plastic stock used to manufacture
lens can also result in slight differences between batches
of seemingly-identical lenses.
- Resolution. Because the lens contains
individual facets, the transition between these individual
facets cause a slight "discontinuity" in the optical
properties of the lens: The smaller the individual
facets are, the more-closely it can (in theory) resemble a
conventional lens and improve its optical quality, making
the individual facets harder to see. It is only
practical to shrink the size of the facts by a certain
amount before the aspects of their individual shapes become
difficult to replicate accurately on a small scale.
- Scattering. Because a Fresnel lens consists
of discontinuities between the individual facets, these
"steps" tend to cause some scattering - particularly of
off-axis light. In general, the smaller the facets,
the worse this problem becomes.
For these reasons, there are a few things for which Fresnel
lenses are not
- Imaging. They aren't very good at being able
to focus an image to fine detail. It is for this
reason that you are unlikely to see Fresnel lenses used on
telescopes and cameras! In addition to this, chromatic
aberration (e.g. "color fringing") is an issue with
such a lens, particularly at lower f/D ratios.
- Not diffraction-limited. One of the limits of
precision of an optical system is related to the fact that
the wavelength of light - although very small - is, in fact,
finite. It is this fact that imposes the absolute limit as to
how fine-focused rays of light may be - even if the lens is
"perfect." If a lens is accurate enough that its
imperfections contribute less
to image degradation than the wavelength of light we refer
to that lens as being "diffraction
limited". Owing to the practical
construction constraints of mass-produced Fresnel lenses, it
is unreasonable to expect performance that approaches
diffraction-limited optics as the methods and materials are
not accurate enough to achieve and hold such accuracy.
- Coherent light. Because of they aren't likely
to be accurate enough to reach the diffraction limit,
Fresnel lenses cannot be used to efficiently and cleanly
collimate a coherent light source such as a laser and
attempts to do so can result in a significant portion of the
light being scattered. It is worth mentioning that
after a laser passes even a short distance through the
atmosphere (a few
kilometers will do it!) it loses enough of its
properties of coherence so that you can use
Fresnel lenses to focus the "formerly coherent" light from a laser onto a
detector at the "receive" end.
Table 1: Calculated
"airy disc" diameters for several representative F-numbers
at 630nm (red) assuming "perfect" diffraction-limited
optics. The lowest F-numbers (below 2.0) are typical
of common Fresnel lenses , the higher numbers are in the
range used in conventional photography while the
highest are typical of those used in "Pinhole"
How good are "ideal" lenses?
the "Airy Disc"
At this point, the question of "How good would a perfect
lens be?" comes to mind.
As mentioned above, one should ideally be able to focus a light
source (such a star)
that is, for all practical purposes,
infinitely distant (and hence its rays parallel) to an absolute
prevents this from happening, resulting in what is referred to
as an Airy
- a fuzzy spot that represents the minimum size
attainable at that wavelength in a lens system - this being due
to the fact that light waves - while very small - are not
Assuming a monochromatic light source with a wavelength of
630nm, Table 1
shows the calculated airy disc size for
several representative F-numbers
(a.k.a. the "F-ratio" or "f/D" radio, the diameter of the
lens divided by its focal length - the terms being used
of "perfect" lenses at that
wavelength. Observe that the theoretical size of the
airy disc is not related to the size of
the lens - just the F-number!
The equation for the approximate size of the airy disc is:
f is the focal length of the
lens being evaluated
d is the diameter of the lens being evaluated
λ is the wavelength of light
x is the diameter of the airy disc in the same
units of measurement as f, d and λ
(Note that the quantity f/d is the F-number!)
So, how close are typical Fresnel lenses to achieving
performance near that of the Airy disc? That's what we
hope to answer.
Types of Fresnel lenses commonly available to the
There are a number of different types of Fresnel lenses
available to the experimenter, but only those that are made of
plastic and can be obtained at reasonable cost either on the new
or surplus market will be discussed here. The vast
majority of Fresnel lenses that are available are equivalent to
lens as depicted in Figure 1
trait common to these lenses is that they are oriented
"grooves-out" - that is, the grooves face the distant object
while the flat side faces the light source (or detector.)
First a warning about all Fresnel lenses!
PLEASE READ the warning to the right concerning
Fresnel Lens safety!
Once you have read it, read it again!
"Giant" Fresnel lenses
A few words about
Fresnel lens safety
Fresnel lenses can be dangerous!
You should always treat a Fresnel lens with
respect - as if it were an open flame!
If you consider that a small magnifying glass and direct
sunlight can burn paper, it is not surprising that even
a rather small Fresnel lens (20x28cm) can concentrate
enough sunlight to instantly incinerate paper, burn wood
and even vitrify
some types of sand! When experimenting with a
Fresnel lens, always treat it as if it
were an open flame - and children should not
play with it unless they are supervised! Even the
briefest exposure of skin at the focal point of a
Fresnel lens exposed to full sunlight can instantly
cause severe burns!
If you store a Fresnel lens, you should always do so in
such a way that it can never be exposed
to sunlight! If, for example, you left a Fresnel
lens in a location where, at some time of day, it was
exposed to the sun and there was something on the other
side of the lens at even approximately the focal
length of that lens, it could be burned when the sun
angle was appropriate.
If you mount a Fresnel lens in a frame, make sure that
it is stored such that it can never be
exposed to sunlight. If you are transporting such
a lens, always carry it in a covered box
or drape it with cloth to prevent it from being exposed
to the full and concentrated energy of the sun!
In other words, an improperly-treated Fresnel lens
can not only burn you, but it can case
severe property damage!
These lenses often appear on the surplus market, many of
which were made for cathode-ray ("tube type")
televisions but are often sold as "fire starters" or solar
ovens. Typically made using flexible optical plastic, many
of these lenses measure around 1 meter diagonally. To use
these lenses effectively they must
be mounted in
a rigid frame as it is imperative that they remain as flat as
possible in order to accurately focus. In other words, you
"hand-hold" them and expect any
reasonable performance - they must
mounted in a frame!
Because they were used for imaging purposes they have quite fine
"groove" pitch (that is, small facet size)
- typically on the
order of 0.2mm. This fine pitch also means that they tend
to scatter a fair amount of off-axis light as there are plenty
of facets to do the scattering in the first place. The
grooves on these fine-pitched lenses are quite fragile and tend
to accumulate dust, further reducing their efficiency and
While the light-gathering capabilities of these lenses are
impressive, the main disadvantage of these types of lenses is,
in fact, their size. They are difficult to transport,
rather fragile, and if used outdoors they tend to act like a
sail and catch every bit of wind - something that makes holding
a precise aim very difficult! Finally, because of their
light-gathering capability, they are even more
potentially-dangerous than smaller Fresnel lenses!
"Page magnifier" lenses
Another source of Fresnel lenses that should not be overlooked
are the inexpensive lenses often found at office supply and
stationary stores that are approximately the size of an A or A4
sheet of paper - 20x28cm or so. These are intended to be
used for magnifying entire pages of text at once and to aid in
reading maps and even though their optical quality isn't extremely high, they do quite a good job.
These "page magnifiers" can be found for anywhere from $1-$15
each - but if you see one for
more than $5, keep looking for a better price!
These lenses are available in two different styles:
- Flexible lenses. Stamped in clear vinyl,
these are flexible and are usually mounted in some sort of
flexible plastic frame to allow them to be kept in a 3-ring
- Rigid lenses. These appear to be stamped in
clear acrylic or similar. Optically, they are
generally equivalent to flexible types, but are quite rigid
and are not intended to be bent.
In order to use the "flexible" Fresnel lenses in an optical
communications system or for collimating a beam/focusing onto a detector they must
be kept flat in order to
assure that they focus properly and to do this one method
involves sandwiching it between two glass plates from a pair of
inexpensive picture frames. When choosing suitable picture
frames make certain that they contain plain, un-frosted
clear glass - and you will want to get two such frames for each
Fresnel lens so that you have two identical pieces of glass for
lens. Once the lens has been mounted between the two panes
and held in position with tape so that they do not slip, the
glass sandwich may be installed in one of the frames which, in
turn, may be mounted in the fixture containing the rest of the
optical gear. My "cheap
" uses this style of lenses in the manner
The rigid lenses have the obvious advantage that could be
mounted in a box directly, without a frame, but it is very
important that they are not inadvertently warped when being
mounted or being subject to the normal stresses of the
box. Even though they are rigid it is worth considering
using a pane of glass in a frame - or at least a sheet of clear
plastic (such as that used to make replacement windows)
- as not
only will this protect the fragile "grooved" side of the Fresnel
from accumulating dust and dirt but it will also reduce the
likelihood that it will be accidentally damaged in
handling. Another advantage of using a frame with a pane
of glass or clear plastic is that this will help to relieve the
Fresnel itself from the stresses of the box being used to mount
the lens that could cause the plastic lens to be warped and
degrade its optical performance.
As will be demonstrated below, the while both are suitable for their
intended task, the optical quality of the "rigid" lenses if much higher
than that of the "flexible" lenses.
The "magnification factor" on the package means nothing!
It is common for these page magnifier lenses to boast ratings in
"powers of magnification" - usually "2x" or "3x". In
reality, these numbers are meaningless
don't have much bearing on what you really
want to know
- and that's the focal
We've noted that these page
magnifier lenses seem to come in two general ranges of focal
lengths: In the 30cm range and in the 60cm range - give or
take a few of centimeters. For practical reasons, which
will be discussed later, you should choose page magnifiers that
have a focal length that is 1-1.5 times the "long" dimension
(e.g. the length)
of the lens that you use which, in this case,
would indicate the use a lens with a focal length in the
general area of 30-35cm.
Typically, these page magnifier lenses are packaged with a
plastic window such that the potential buyer can test them prior
to purchase and this lends nicely to being able to determine the
focal length in the store, before
them. To check their focal length, simply hold the lens up
and focus the lens onto a piece of paper, measuring the distance
between the lens and the paper, but when you do this make sure
that the grooved side is pointed away
paper and that you pick as distant an object to focus as you
can: If the store has windows, try to focus the scene
outside using a distant object. Note
sometimes these lenses are sold as pairs with two in a package
and unless you can test just one
of these lenses
at a time (which would probably mean opening the package)
above test won't work!
Overhead projector lenses are usually terrible!
One potential source of Fresnel lenses for experimenters have
. Typically, these lenses are built into
the plate onto which the transparency is laid, with the Fresnel
lens being used to direct the light upwards toward the
right-angle mirror or lens assembly and onto the screen.
Unfortunately, these lenses are NOT
suitable for purposes of collimation or the focusing of a
distant light source onto a detector as they may not be
designed to focus at infinity.
main purpose is usually that of concentrating the light from the
projection bulb and not
forming an image directly, they
do not function as needed and often blur and/or scatter light
should they be attempted to be used.
"Computer Monitor Enhancement" lenses
One possible source of Fresnel lenses are those sold to enhance
the computer-gaming experience. By placing a Fresnel lens
in front of a computer monitor one can achieve the illusion of a
much larger monitor and field of view than is actually
present. These types of lenses are often somewhat larger
in size and with smaller facets (to improve image quality)
those of page magnifier lenses and some of the lenses sold by
3dlens.com (including lens #1, the "F550" tested below) are
marketed for such purposes.
There are a number of suppliers that specialize in Fresnel
lenses and some of them are of very high quality.
Unfortunately, when purchased new, these lenses can be quite
expensive compared to the inexpensive page-magnifier types -
that is $30-$100 as compared to $1-$15 for a comparable-sized
page magnifier. Occasionally, these high-quality lenses
show up on the surplus market, but these sources tend to be
intermittent and you must be certain that you know exactly
what you are getting!
As with traditional glass lenses, Fresnel lenses can be made to
have both positive and negative focal lengths and have a variety
different optical properties. If you wish to buy a lens
for optical communications it is recommended that it be as
square as possible, optically equivalent to a plano-convex
lens (and therefore have a positive focal length)
with the grooves facing outwards, designed for being focused to
infinity, have an F-number of around 1, and be made from optical
acrylic or a similar material.
For a partial list of sources of various types of lenses,
see the "Optical
Sources" page at this web site.
"Grooves out" versus "Grooves in"
Most commonly-available Fresnel lenses are "Positive" lenses
that function as a Plano-Convex lens as depicted in Figure 1
above. While many different configurations are possible
most of these lenses are made so that the grooved side goes
- that is, the "grooved side" goes away
from the LED or detector.
In the unlikely event that you find a "Grooves in" (that is, the
"grooved" side goes toward the LED)
type of lens, this property
can be readily demonstrated by focusing a distant outdoor scene
onto a white piece of paper or wall. If one tries the lens
both ways (e.g. grooves out and grooves in)
orientation will be apparent with an image that is sharper
and/or brighter than can be had when the lens is oriented the
Note that in a casual test it may seem
Fresnel lens may focus well either grooves-out (toward infinity)
or grooves in, but a careful examination will reveal that this
is not the case: The proper orientation can be determined
simply by focusing an outdoor scene (through a window)
white sheet of paper or a wall and noting that one direction
provides a better (sharper image, improved contrast)
other way: A nighttime scene with points of light (e.g.
is helpful in that an improperly-oriented lens can
cause fuzzy halos to appear.
Practical optical systems using Fresnel lenses
For practical reasons, it is recommended that an optical
system using Fresnel lenses be designed using lenses that
have an F-number
in the range of 0.5 to 1.5 - that is, around 1. Remember:
The "F-number" is the focal length divided by the diameter of
the lens, so for an F-number of unity or one, the "diameter" of
the lens would be approximately the same as its focal length.
What's the "diameter" of a
square or rectangular lens?
Most Fresnel lenses aren't round!
Because the F-number is the ratio of the focal length
divided by the diameter of the lens, how do we express
the "F-number" of a "non-round" lens?
For the purposes of this web site, the F-number is
generally based on the "wide" dimension of a rectangular
lens - but not from corner-to-corner.
So, if we had a lens that had a "grooved area" of 268mm
by 200mm with a 330mm focal length, we'd generally say
that the F-number was 1.23.
Why the recommendation of this F-number range?
The main consideration is that of practicality. Consider a
hypothetical lens with a diameter of 30cm. With an
F-number of 1, the focal length will also be 30cm, and if you
were to construct a box that contained both the lens and, say, a
detector at the focal plane, it would be about 30cm in
length. From a practical standpoint such a box (which
would be roughly cube-shaped)
would be of a manageable size and
wouldn't be too difficult to handle.
Consider, then, a similar lens with an F-number of 5. If
we take this same lens - one 30cm in diameter - we will have to
place the detector of our hypothetical box 150cm (nearly 6
away from the lens: It is easy to see that such a
structure rapidly becomes quite large and cumbersome, requiring
a lot of material and it would be difficult to transport!
Because Fresnel lenses aren't constrained in their design in the
same way that traditional lenses might be it is perfectly
reasonable to construct a Fresnel lens with an F-number of
unity: Indeed, Fresnel lenses are commonly available with
F-numbers from 0.5 to 4 or so. From a practical
standpoint, most inexpensive Fresnel lenses are made to have
F-numbers in the range of unity to 2: Too-small an
F-number and one runs into practical considerations related to
the refractive index of the material used for the lens as well
as the geometry of the facets, while a higher F-number implies
increasingly-greater precision of the lens and its dimensions in
order to maintain a precise focus - both being factors that
translate to greater cost in manufacture
Another reason for the recommendation of this F-number range
relates to using the lens in an optical transmit/receive system
and this could be the basis of an article it its own right, so
only a few of the details will be discussed here. For
transmitting this has to do with being able to efficiently
the light from the LED to the Fresnel itself - usually through
the use of a "secondary" lens being used to narrow the beam of
light to "illuminate" the back of the Fresnel. If the
F-number is larger - above about 1.5 - this becomes increasingly
difficult to do with a simple secondary
owing to the need to use an increasingly "stronger" (smaller
secondary lens next to the LED as the F-number of the
Fresnel lens system increases: At some point the F-number
of the required single secondary lens gets too small to be practical.
At the other extreme (e.g. smaller F- numbers - in the area of
the problem becomes largely one of geometry. One
problem that such an F-number implies is that a wide
illumination angle is required from the perspective of the
emitter and this means that the edges of the lens are
significantly more-distant from the emitter than the center of
the lens. This difference in LED/Fresnel distance
increases the amount of "falloff" in the amount of light that
gets to the edges of the lens, potentially making the system
less efficient. For reception, it's also worth noting that
the responsiveness of many detectors decreases when the incident
light arrives at angles far-removed from the center axis.
for through-the-air optical communications
Transmission and collimation:
It is also possible to use a Fresnel lens as a collimator
- that is, an optical system to produce highly-parallel beams
like those of a spotlight as seen in Diagram 2
noted before, the imprecise nature of a Fresnel lens precludes
their efficient use to efficiently collimate coherent
(such as that from a laser)
as an inexpensive, molded Fresnel lens may not practically be
made to be accurate enough to be diffraction-limited
light will likely result in a significant percentage of that
light being scattered rather than being collimated.
Figure 2: This diagram
shows a Fresnel lens being used to collimate light from an
LED. In "reverse", it can be used to concentrate
parallel rays of light from a distant source onto a
detector. Also shown is the effect of the source
size on overall beam divergence. In a practical
system, a "secondary" lens would be placed very close to
the LED to reduce the angle over which the LED's light was
cast to allow a much greater percentage of it to reach the
As readers of this, the modulatedlight.org
site, are already aware, we extensively discuss the use of
non-coherent light sources (such as LEDs)
communications systems and Fresnel lenses are nicely suited for
The "ideal" shape of a Fresnel lens would be one that is round
this would match the shape of the circle of light that is
typically emitted from an LED/secondary lens emitter
assembly. Departures from this "round" shape imply a loss
of light owing to some portion of that circular "pool of light"
being projected onto the backside of the lens being cut off
along the edges with this loss of efficiency becoming even worse
as the lens is made more-strongly rectangular. Since it is
rather rare to find a large, round Fresnel lens on the surplus
market - and due to practical difficulties in mounting a round
lens - square or rectangular lenses are, by far, the most
common. It's worth mentioning that the shape of the lens
is not particularly important when used for receiving
the shape of the spot of light being focused onto the detector
has little to do with the aspect ratio of the lens.
As previously noted, when using an LED (or other light source)
with a Fresnel lens it is generally necessary to use a secondary
lens (between the
emitter and the Fresnel)
to match the beam characteristics of
the emitter to the apparent subtended angle of the Fresnel as
"seen" from the viewpoint of emitter assembly. While
adding this lens necessarily increases the apparent
size of the
emitter, the loss of efficiency due to the subsequent increase
of divergence is usually much more
than offset by the increased overall
efficiency of the system as a whole. Unfortunately, a more
in-depth discussion of this topic is beyond the scope of this
page but can be discussed with the author via email.
Reception and detection:
For optical communications it is desirable to use a large an
aperture lens as practical to intercept as much energy as
possible from the distant light source. In addition to
intercepting this energy it is also desirable that the field of
view be reduced in order to reject off-axis light sources that
could degrade the communications link.
The question arises, then: "How good is a typical molded
Again, while not generally suitable for imaging, analysis of the
quality of the image produced by these lenses when observing a
point source of light can be instructive in determining a few
qualities of its construction - namely the accuracy of the
facets comprising the lens. For optical communications
purposes where radiometric
is employed - that is, energy from the distant
source is detected, generally irrespective of its specific
wavelength - light from the distant source is focused onto the
active area of the detector, producing an electric signal that
is then amplified.
It makes sense, then, that it is desirable that as much of the
light being intercepted by the lens gets focused onto the
detector and that as little as possible of this light is wasted
by "missing" the detector. To accomplish this a "minimum"
size of detector is implied - that is, if the area of the
detector is much smaller than the spot produced by the lens when
it is optimally focused, then not all of the light from the
distant source will strike the detector and contribute to its
detection resulting in unnecessary loss of detection efficiency.
Conversely, if the detector is too
large, there are two potential
problems: A larger detector implies a wider field of
which means that it is likely that stray energy from
other sources of light that are off-axis may fall across the
detector, possibly "diluting" the desired signal source.
The other problem is that a larger detector (particularly a
photodiode) can have worse
sensitivity than a smaller diode as the larger device will
likely have a higher capacitance and higher intrinsic noise than
a small one. In other words, it's not usually beneficial
to have a diode so large that only a small portion of its active
area gets illuminated by the distant light source!
Note: A large aperture lens also reduces
the effects of scintillation of the detected signal due, in
part, to the fact that a larger lens offers a degree of spatial
diversity. A large lens also minimizes effects of
"local coherence" - another potential contributor to
Another question that arises in this discussion is: How
efficient is an optical system using a Fresnel Lens as compared
with one of equal size using glass lenses? This is a
difficult question to answer and the estimates that I have seen
seem to vary.
High-grade optical acrylic can have very low transmission loss
at the design wavelength - roughly comparable to glass.
Considering that far less material would be used in a Fresnel
lens than a "conventional" glass lens of similar optical
properties (e.g. the Fresnel would be much thinner)
less material contained within the Fresnel to contribute to
Another factor having to do with efficiency is the fact that a
Fresnel lens consists of a number of facets. At their
transition points, some degree of loss (largely through
occurs due to these facets - the problem being
arguably worse with increasingly-fine "groove pitch" lenses, not
to mention the accuracy and "sharpness" of these facets.
Finally, there is the issue of accuracy of the lens
itself. Since a Fresnel lens cannot achieve the precision
of a high-quality glass lens it is safe to assume that it cannot
focus nor collimate a beam as tightly as an ideal lens.
This, however, does not actually affect the light-gathering
ability directly as if one uses a suitably-large detector, all
of the light from the distant source can still be intercepted -
albeit over a larger focused area. What it does
affect is the minimum field of view (in the case of the
and divergence (in the case of the emitter)
system - both being factors that can affect the performance of
the system to a degree but not necessarily its absolute ability
to gather/emit light.
If we were to assume that a Fresnel-based system were only 50%
efficient as compared to a similar-sized glass lens (a number
that is likely pessimistic with high-quality Fresnel lenses)
should be remembered that this deficiency could be compensated
by using a Fresnel lens that was 1.4 times the diameter (hence
twice the area)
of the glass lens. Because of their light weight
and low cost, constructing a receiver that used a larger Fresnel
lens to make up this difference would be quite practical while
in the case of the transmitter, the larger exit aperture would
be of benefit in minimizing the effects of scintillation and
could, to some extent, reduce divergence.
When used with an emitter it is desirable that the divergence be
minimized in order to achieve the highest-possible far-field
flux (brightest light)
at the greatest distance. As with
any type of lens or reflector, the amount of divergence is
related to the inverse ratio of the area of the emitter versus
the area of the lens being used to collimate. In other
words, the tiniest emitter plus
the largest lens
will result in the lowest amount of divergence!
In a laser pointer, good collimation occurs because the laser's
emitting area is only a few 10's of microns across. This,
coupled with the fact that the lens is going to be a few
millimeters in diameter implies a pretty good "lens/emitter"
area ratio. In an LED-based system, a typical high-power
LED can be millimeters
in size so it's not too
surprising to note that an extremely high "lens/emitter" ratio
would imply a large Fresnel lens, indeed! As will be
demonstrated below, the divergence of a lens system using
Fresnels is probably going to be set by the actual size of the
emitter itself rather than the quality of the lens!
What can we learn by
knowing the size of the "blur circle?"
Because a Fresnel lens is unlikely to approach the diffraction
limit at visible wavelengths it would be improper to refer to
the minimum "spot" size produced by such a lens as an "airy
disc" - that is, a pattern resulting from the wave properties of
the light itself. To describe the smallest "spot" of light
that we get with an "imperfect" lens we'll use the phrase "blur
" - a term akin to the "circle
What, then, can we determine by analyzing the lens's blur
- How good is the lens?
from a distant light source can tell us something about the
quality of the lens being tested.
- What is the minimum
recommended size of the detector? By knowing
the area over which the light can be focused can tell us
something about the size of detector we would use.
By knowing the above, another question can be answered:
- Is the divergence of the
collimated beam set by the size of the emitter, or the
quality of the lens? In any collimated system
the divergence is set, at least in part, by the ratio of the
aperture size and the apparent size of the emitter. If
the surface area of the emitter being used is somewhat
larger than the blur circle, one can be reasonably sure that
the divergence of an optimally-focused collimator system
will be set primarily by the size of the emitter rather than
the quality of the lens. Conversely, if the emitter's
area is much smaller than the blur circle, it is
likely to be the quality of the lens that will dictate the
Not surprisingly, plastic molded Fresnel lenses are not
well-characterized in terms of their image accuracy so the
relative size of the "blur circle" must be determined
determination the size of the blur circle:
Determining the number of
pixels per millimeter:
Fortunately, it is practical to measure sub-millimeter
spot sizes with reasonable accuracy. Using a digital
imager of known dimensions it is possible to ascertain the
approximate dimensions of a the blur circle by analyzing the
resulting picture. For this I used a high-sensitivity "CS mount
video camera with its lens removed and a video capture device on
a laptop computer. With this setup, real-time images can
be displayed on the computer's screen while the
Fresnel-to-imager distance and angles are adjusted for optimal
focusing and planar alignment, projecting the image from the
lens directly onto the imager. Once the adjustments are
made, the image is then digitized and notations made for later
analysis. When making final measurements, remember that
it's the size of the final
image after digitization and not
the actual resolution of the imager that should be considered
when calculating the number of pixels per millimeter. When
using an analog video camera and digitizing the result it's
usually the case that the resolution of the captured image
doesn't exactly match the resolution of the imager!
For some cameras determining the actual
size of the imager's "active area" and
from there, the size of the pixels, can be difficult as
described in the article, "Making (some) sense out of sensor
" Fortunately, with CCTV cameras
intended for use with standard "CS" (or "C" mount) lenses, the
"size" of the sensor is typically spelled out in the camera's
specifications and from that it is possible to work backwards
and determine the number of pixels per millimeter of the
imager. For example, for a standard "1/2" CCTV imager the
active area is typically 6.8mm x 4.8mm and from this, it is
possible to estimate the pixel size of the resulting image.
If a DSLR with a removable lens or a modified webcam is used
instead of a CCTV-type camera you are on your own to determine -
as best you can - the physical dimensions of the imager's active
area and thus the image's pixel's "pitch." Finally, be
aware that not all cameras/digitizers produce "square" pixels.
Source of light - Star:
In order to properly test a lens that is to be used for
collimation or detection, an infinitely-distant, point-source is
ideal as an light source as it would push a "perfect" lens to
its diffraction limit. Assuming that the pixel size of the
resolve the size of the blur circle of the Fresnel lens (an assumption that we'll make for
that leaves us with the selection of the
One group of possible light sources may be found in the night
sky: Stars and planets. Stars definitely fit the
bill when it comes to being adequately-distant, point-sources of
light, but their use has several drawbacks:
- They are usable only
during a clear, cloud-free night. This is
obvious and isn't as much of an inconvenience if you live in
a desert like I do, but it does limit when - and to some
extent, where - testing can be done - that is, nighttime and
not during winter!
- They usually "twinkle."
the brightness (and, to some extent, the apparent position)
of a star can vary randomly due to atmospheric
effects. This can complicate measurements, as you
- They aren't usually
located at convenient elevations. It is more
likely that a star will be located at a rather awkward angle
in the sky. Practically speaking, it is preferable to
have a light source either straight up (at the zenith) or
on the horizon (which is unlikely!) as those locations make
mounting and adjusting both the lens and camera most
- Stars are always
"moving." Once you get everything lined up -
which, itself, is not an easy task - the rotation of the
earth will cause the star's apparent position to drift
off. Clearly, this movement complicates setup of the
lens and the subsequent capturing of an image.
- Starlight is not
monochromatic. Because a Fresnel lens is a
rather simple lens, it suffers from Chromatic Aberration
which means that white light is separated into its
constituent colors, spreading the image and making precise
alignment (e.g. focusing) more difficult - a fact
exacerbated by the short F-number
of typical Fresnel lenses. Practically speaking, one
can place a color filter in front of the imager and/or do
some post-measurement image processing to remove certain
colors to reduce this effect.
Having used the "star" method I can attest to that fact that
while it does work, it's very awkward for all
the above reasons! One of the greatest difficulties can be
the initial alignment - that is, finding the initial focus of
the lens and determining if the star's image is in focus.
When doing this I have used the star Vega
conveniently near the zenith at reasonable hours during summer
nights in North America and is bright enough to produce a
visible dot when projected onto a piece of white paper - a trick
which helps determine the focal plane and alignment of the lens.
Figure 3: The
"non-infinite" light source used to test the lenses.
Click on the image for a
Instead of stars, it is possible to use planets. Using a
planet as a "point source" has the advantage that it can,
depending on the planet and its distance, be much brighter than
most stars, and its subtended angle is sufficiently large that
it is less-likely to twinkle, but they are bright enough that
one has to be careful to not
saturate the imager being used and make precise adjustment and
subsequent measurement difficult. Unfortunately - like
stars - you need to constantly track them! Another
consideration is that because of their large apparent "size"
(owing to their relative nearness when compared to stars) they may
not be small enough to
sufficiently test the lens to its limits.
Using the above method and using the star Vega I was able to determine that the blur circles of the
Fresnel lenses that I have are
more than large enough to be discerned with a CCTV camera's
imager - a fact that confirmed that it should be possible to
make reasonably accurate measurements.
Source of light -
Using a star and having determined that a CCTV
imager had more than adequate resolution to measure a typical
Fresnel lens, attention was paid to the possible use of an
artificial light source for testing. Much more convenient
than relying on a properly-positioned, moving star on a clear
night, an artificial light source would allow repeatable
measurements but the question was "How does one simulate an
infinitely-distant point-source to adequately test the lens?"
As it turns out one doesn't need to have such a light source to
test a Fresnel lens. Rather than being infinitely-distant
(which would be very
a light source with a small subtended
may be placed relatively close to the lens to
adequately determine its "blur circle" properties. By
producing one's own light source it is also possible to make it
monochromatic (e.g. one color)
to minimize chromatic aberration
of the lens being evaluated as well as testing the lens at the
wavelength for which operation is anticipated.
To produce a "spot source" of light I constructed the device
shown in Figure 3
Using a 0.25mm drill bit,
I made a hole in a 0.15mm thick piece of sheet brass. In a
small, light-tight box made from double-sided printed circuit
board material I enclosed a high-brightness red LED (a Liteon
P/N: LTL912SEKSA, which is also a Radio Shack #276-020)
soldered to the box - covering a larger hole - the piece of
brass with the 0.25mm hole which was aligned with the LED.
Also contained within this box is a simple current regulator
connected to a switch that allows either 60mA or 2mA of LED
current to be selected: The high-current setting provides
enough light, using a white piece of paper, to establish the
aiming and rough focus of the Fresnel lens onto the camera's
imager while the low-current setting prevents saturation of the
camera's imager and makes final focus easier. This device
also has 1/4"-20 threads tapped into a bottom hole to allow it
to be attached to a standard tripod mount.
Even though the 0.25mm diameter spot of light is only about 15
meters away (hardly "infinitely distant"!)
and the focus of the
lens being tested is slightly "off" from what an
infinitely-distant source would be, the results have been
compared, using some of the same lenses, to those obtained using
the star Vega and they seem to agree nicely indicating that this
should be a reasonable method of ascertaining lens quality -
especially since we are hardly likely to approach the
diffraction limit with these lenses, anyway!
Methods that use lasers:
Before anyone else mentions it, I'll point out that I am aware
of methods using lasers to test the focus and quality of lenses
but I dismissed these methods for testing these lenses for a
number of practical reasons: If you are already familiar
with these methods then you'll appreciate the implied difficulty
of testing large aperture plastic lenses with many facets!
4: Some of the lenses tested on
this page. In order, from left to right/top
to bottom are lenses 1-9.
Click on the image
for a larger version.
- When interpreting these results, the absolute brightness
of the images is less-important than the size and
shape. Because camera imagers are not linear, it is
not possible to make accurate determinations of absolute (or
- As can be seen, each image includes a scale to allow the
viewer to relate the image size to 1 millimeter, allowing an
estimation of the size of the spot. Note that the size
estimations are somewhat subjective and approximate.
- Noted in each of the descriptions is the approximate
"F-number" of the lens. Because most of the lenses are
rectangular rather than being round or square, the F-number
given is always based on the long
dimension of the lens. This is done because, when used
as a collimator, it is generally best to treat the lens as
if it were round with the diameter
approximately equal to the long dimension. The
reasons for that are beyond the scope of this page, but if
you want to know you can always drop an email to the
address linked at the bottom of this page.
Comment: In theory, it should be possible to
"re-linearize" the brightness (to compensate for the
intrinsic "gamma" of the camera) of the pixels in the
resulting images and make an estimation of the amount of
light energy contained in a particular unit-area of the
spot. This could be used to determine, with reasonable
accuracy, the various sizes/areas in which different
percentages of the total amount of energy, that the spot
Figure 5: "Blur
Circle" of the 3dlens.com M/N: F550.
Lens #1 - 3dlens.com Model #F550:
This Fresnel lens is 320mm x 400mm with a focal length of
Click on the image for a larger version.
This lens is sold by 3dlens.com
in Taiwan and is
available via the internet, shipped by mail. This lens is
constructed of optical acrylic, it is 320mm x 400mm, 2mm thick,
has a "groove pitch" of 0.2mm, a focal length of 550mm and is
approximately 2mm thick.
As can be seen from Figure
5 the vast majority of the light is concentrated
into an area under 1mm diameter although some of it is
scattered across a larger area. Visible in the picture
is a slight amount of coma
owing to the fact that distant light source was slightly
higher than the center of the lens, but the image is "pretty
close" to the optimal image obtained. (I should probably re-do this
With an F-number of about 1.375 this lens is a bit on the
"long" side of what I recommend.
Fresnel lenses with fine groove pitches (the 0.2mm pitch of
this lens is considered to be fairly fine) tend to have
greater scattering losses than "coarser" lenses owing to the
greater number of facets over the surface of the lens.
These scattering losses can decrease the rejection of
off-axis light sources as well as somewhat increasing its
Compared to the other lenses tested, the performance of this
lens was somewhat disappointing as the size of the blur circle
is a bit larger than expected. Practically speaking,
however, this lens would work well in a system using an LED of
several square millimeters in size and a detector of the size of
"Blur Circle" of a 250mm x 318mm Fresnel lens with
a 229mm focal length.
Click on the image for a larger version.
#2 - Surplus Shed L3606 (229mm F.L.):
The second lens was obtained from SurplusShed.com
(P/N: L3606) and is 250mm x 318mm and is also made
from optical acrylic about 2mm thick.
While the manufacturer of this lens is unknown, it appears
to be of high quality but (unfortunately) their supply of
this lens has been depleted. I ordered this model
number of lens on two occasions and the first time, I
received lens tested below (#10) - but after successfully
using that lens in my first
enclosure, I ordered some spares. Interestingly,
the "new" lenses - although the same size and with the same
part number, had a 100mm shorter
focal length than the others - about 229mm.
As can be seen, the lens produces a spot that is
significantly "denser" than that of lens #1 - a trait due,
at least in part, to its much-shorter focal length.
This lens has an F-number of about 0.72 which is short, but
The groove pitch of this lens is "medium" at approximately
0.5mm which reduces scattering losses as compared to
Figure 7: "Blur
Circle" of a "Page Magnifier" lens.
This Fresnel is about the size of a size "A" (or A4) sheet
of paper and has a focal length of approximately 330mm.
Click on the image for a larger version.
Lens #3 - Rigid "Page Magnifier" from an office supply
The third lens is rather interesting: It is an
inexpensive lens, sold as a "page magnifier" obtained from American
and Surplus and was Stock #38939 (no longer
available.) This lens is 213mm x 280mm, about
2mm thick with a clear "border" around its edges, resulting
in "lens area" of about 268mm x 200mm. These
types of lenses may also be found at office-supply and
stationary stores and the occasional bargain shop or
"dollar store" - or even online (e.g. Ebay, Amazon),
often under the brand name of "Bazic" described as a
"Full Page Magnifier" with "2x" magnification as part
With a focal length of about 330mm, it has a
moderate F-number of 1.23 (based on the "long" dimensions of the
lens's "active" area) and a groove pitch of around
0.5mm. This image in Figure 7 is very
slightly misfocused (which explains the dark spot in the
center of the blur circle) but the size of the spot is
As can be seen in Figure 7
this lens produces a nice, tightly-controlled spot of light
due, at least in part, to its relatively small size (that
is, there is "less" of the lens present to be
inaccurate.) The performance of this lens -
even though it is very inexpensive - is surprisingly good,
especially considering that it was intended solely as a
"full page magnifier" where significant optical distortion
would not otherwise detract from its intended use.
Having had the opportunity of briefly examining several
different types of these lenses I've noted that they are all
about the same size (varying a few only a centimeter or so
in each dimension), approximating a sheet of "A-size" (or
"A4" size) paper with the exact dimensions depending on the
supplier. We have noted that there are two distinct
ranges of focal length: 300-350mm (usually in the
320-350mm area) and around 620mm - but it is only this
lens (approximately 330mm F.L.) that I have had the
opportunity to test!
It should be noted that the longer focal-length versions
(around 620mm or 24") are not as useful for optical
transmitters/receivers as the shorter focal-length lenses
for several two main reasons:
- A 620mm focal length implies a fairly large structure -
long enough to accommodate the lens and the electronics at
the lens's focus. Such a box is large enough to be
awkward to be constructed and transported.
- A large F-number of about 2.3 makes it very difficult to
efficiently couple the optical output of typical high-power
LEDs to the lens. Again,
the reasons why larger F-numbers are less desirable for
transmit use are beyond the scope of this page - email me
for further information.
Fortunately, these lenses are usually display-packaged in clear
plastic so it is easy to test them without opening them and
annoying the sales staff: A distant object (preferably
outdoors and more-distant as to obtain an accurate measurement)
is then focused onto a surface and the focal length
measured. The downside of these types of lenses is that
they are more rectangular than square, having an approximately
1.33:1 aspect ratio. What this means is that in practical
use, a larger portion of the circular pool of light from the
illuminating LED is lost along the "long" edge (that is, the
and causes a decrease in overall system
efficiency. If you are really
careful, it is
possible to make very precise cuts and use portions of other,
identical lenses to increase the size of the "narrow" dimension
- but if you were wont to do this, you might was well get a
larger, "squarer" lens from another supplier, anyway!
Because of its reasonably good
quality and low price I would consider this to be an excellent
lens for optical communications work - if you can find one like
it! The folks in the UK, having built quite a few optical
systems using these sorts of lenses, have had quite good luck
and consistent results (as long as they used lenses with
focal lengths in the 300-350mm range)
consistent quality across different brand names. I have
also constructed some LED transmitters with these lenses and
they have produced good, parallel beams.
"Blur Circle" of a 260mm square Fresnel lens with
a 200mm focal length.
Click on the image for a larger version.
Lens #4 - 3dlens.com
This is another optical acrylic lens sold by 3dlens.com and is
260mm x 260mm with a focal length of 200mm with a groove pitch
of 0.2mm and a thickness of about 2mm.
This lens also has a nicely-controlled blur circle and a fairly
short F-number of 0.77. When used for transmitting, a
square lens is somewhat more efficient than a rectangular one
because less of the circular light projected from the source is
cut off along the edges.
The F-number of this lens is quite low, but it is perfectly
usable. The only downside of this lens is that the groove
pitch is 0.2mm, which slightly increases scattering losses.
Figure 9: "Blur
Circle" of a 395mm square Fresnel lens with a 220mm focal
Click on the image for a larger version.
Lens #5 - 3dlens.com
Product # A395b:
This is yet another lens from 3dlens.com and 395mm x 395mm, with
a focal length of 220mm, a groove pitch of 0.5mm and is
constructed of 2mm thick optical acrylic. As can be seen
from figure 5, this lens also produces a reasonably good-quality
The F-number of this lens (0.57)
is low, making it a bit of a
challenge to use, but it can offer excellent results with proper
For some reason this lens has rounded corners - a factor that
slightly complicates its mounting in a frame as those corners
would allow dust to enter and air to pass through - although it
would be pretty easy to seal the corners with plastic or
cardboard or (carefully!)
cut it down to a smaller, square-cornered size which would also
effectively increase the F-number. As with lens #4,
because this lens is square there will be lower transmission
losses from vignetting of the round pool of light along the
edges than would be the case with a rectangular lens.
"Blur Circle" of the Anchor Optics 27363 Fresnel
lens. Unfortunately, a slight amount of coma
was captured in the image during testing.
Click on the image for a larger version.
Lens #6 - Anchor
This unusual-looking lens is round, with an active area of about
335mm in diameter with a groove pitch of about 0.5mm. This
lens appears to be on its original factory "blank" - that is, it
would seem to have been intended that a square lens of 285mm per
side (with an "active" area of 270mm, square, bounded by a
border that is about 8mm wide)
be cut from it. The focal
length is approximately 230mm.
This lens appears to be of good quality and as can be seen from
, it produces a
nice, tight pattern. In the image I managed to catch a
little bit of coma due to a slight misalignment, although that
is not an intrinsic property of the lens.
This lens is apparently a surplus item sold by Anchor Optics -
but they seem to have a reasonable supply of them as it shows up
frequently on various optical-related forums.
Interestingly, the online catalog lists this lens as having a 15
focal length - but the samples that I have are
definitely closer to 230mm! I'm not sure if they
mis-measured the focal length, or if there are a number of the
same-sized lenses in their stack with different focal lengths!
With an F-number ranging from 0.69 (if you consider the diameter
of the grooved section )
to 0.85 (if you only consider the
it has a fairly short - but useful -
ratio. The coarse grooves minimize scattering losses
making it a reasonable lens for both transmission and
reception. Because of it's square/round shape, optical
transmission systems constructed using it are more efficient as
a smaller amount of the circle of light from the LED is
truncated along the edges than would be the case with a
I would consider this to be an excellent lens for optical
Important comment about surplus Fresnel lenses:
As is occasionally the case with surplus Fresnels,
different focal-length lenses may be mixed together -
particularly if they have similar physical dimensions and do
not appear, at first glance, to differ from each other.
Such may be the case with some of the lenses from Anchor
Optics: As noted above, the catalog stated that this
lens had a focal length of 381mm but my sample was closer to
230mm - and the observation that the lenses received differ from the catalog
specifications has been reported to me by at least one other
Figure 11: This is the
"blur circle" of the AX70877 lens - but it was so faint
that the image had to be considerably
enhanced to see it. Click here
to see the original (and very dim) version!
Click on the image for a larger version.
Lens #7 - Anchor
Not all Fresnel lenses are created equal - which is to say that
not all of them are made for the same purpose. This lens -
the Anchor Optics AX70877 - was apparently made for Overhead
use or as some sort of large condenser
lens. It is common, with these types of lenses, that they
be designed to focus at infinity
which means that one shouldn't be surprised to see that they
perform poorly when called on to do so!
This lens is 283mm square (with cut-off corners)
with an active
area of about 265mm square with a groove pitch of between 0.35
and 0.5mm and about 2mm thick. The focal length - when one
attempts to focus it at infinity - is around 390mm, but since it
does not focus well at all this measurement is only
approximate. Made by a company called "Cryton Optics Inc."
of Roslyn, N.J. it appears to be of good quality - but just not
the sort of thing you would use for focusing anything at
infinity - or even 15 meters!
As is seen in Figure 11
this lens produces a fairly large spot - but that's not the
entire story: Much of the light focused onto the image was
actually spread out over a far larger
area than the imager and is
below the its threshold of sensitivity - but clearly visible
(and covering more than the entire face of the imager)
LED current was turned up to maximum and the picture was
enhanced (which brought up the noise considerably)
to show the
very dim details.
Figure 12: The
"blur circle" of a rather long (610mm) focal
length Fresnel lens. Even though the spot is
quite large, it is quite reasonable when compared
with its focal length.
Click on the image for a larger version.
Lens #8 - Surplus
Shed L3707 (610mm F.L.)
Some time after building a box to use lens #10 (below)
to order some spare lenses. Unfortunately, they were sold
out - but they had one of these (610mm F.L.)
lenses onhand, so I
decided to get it anyway out of curiosity. When it arrived
I could see that it was of the same, high quality as the
identically-sized lenses (#10)
- just a different focal length.
Even though the F-number is a somewhat long (but reasonable)
1.42, this focal length would imply that the box or mechanical
assembly used to hold the lens and electronics would be quite
large. Properly "illuminating" this lens with an LED would
be a bit of a challenge, but it would make a nice lens for a
receiver - provided that the photodetector was large
enough: A BPW34 would work nicely!
Figure 13: This is the
"blur circle" of the flexible Fresnel lens.
Click on the image for a larger version.
Lens #9 - 3dlens.com
Product # 406f:
This is another of the "Page Magnifier" lenses - but instead of
optical acrylic it is made from much thinner (approx. 0.4mm)
clear, flexible vinyl with a groove pitch of 0.3mm.
This particular lens includes a "frame" of black, flexible vinyl
to permit mounting in a 3-ring binder and to allow handling
without touching the lens area and is about 194mm x 270mm (with
a 35mm long "handle) and a lens area of 158mm x 222mm.
Because this lens is flexible, it is necessary to hold it flat
(against, or sandwiched between pane(s) of glass or acrylic)
order for it to focus properly.
As can be seen from Figure 13
this lens would appear to have comparatively high scattering
losses, but considering its intended purpose this is not too
surprising! Admittedly, during this test I may not have
held the lens as "flat" as it should have been so it's on my
list of lenses to re-test some time in the future.
Lens #10 - Surplus
Shed L3606 (330mm F.L.)
This is the "blur circle" of the 250mm x 318mm
lens with the 330mm focal length.
Click on the image for a larger version.
When I ordered lens #2, it was intended to be a spare for this
lens, but as
mentioned, it wasn't of the same focal length as this one!
This lens was obtained from SurplusShed.com
(P/N: L3606) and is 250mm x 318mm and is about 2mm
thick with a focal length of 330mm and a groove pitch of
about 0.5mm. (As
you have probably guessed, the stock of this surplus lens
has been depleted.)
As can be seen from Figure 14
this lens produces a very "tight" spot of light - arguably
better than any of the other lenses tested. Due to a variation in the setup
the image in this figure is somewhat darker than those above.
Lenses of this type were used in my First
Figure 15: This is the
"blur circle" of the 404mm x 430mm lens with a 229mm focal
Click on the image for a larger version.
Lens #11 - Surplus Shed L3707
This is the lens for which lens #8 was ordered as a spare, but
the Focal Length was different.
The story gets rather complicated at this point: On the
Surplus Shed web page this lens had originally been listed as
having a 24 inch (610mm)
focal length, but when I got them, I
saw that they were around 229mm (approx. 9 inches.)
turned out for the better as the 9" focal length - although a
bit short of an F-number - made for a rather compact enclosure
for a lens of this size while the originally-stated focal length
would have required quite a large box! Now,
before anyone gets the idea that the folks at Surplus Shed
didn't have their act together, it should be pointed out that
they weren't aware that these identically-sized Fresnels seemed
to have come in different focal lengths until someone (not me!)
pointed it out. By the time they realized this (and
changed their on-line catalog)
they had more-or-less depleted
the stock of lenses for which I desired spares.
Anyway, this lens, like #8, is 404mm x 430mm and 2mm thick with
a 0.5mm groove pitch. Unlike that lens, this one has a
229mm focal length, meaning that it has an F-number of 0.53 -
shorter than that of lens #5. As can be seen in Figure 15
this lens produces
a nice, tight spot of light. As with lens #10, a variation in the setup resulted
in a somewhat darker image than many of the above images.
The short focal length of this lens makes its use slightly
awkward, but I have very successfully use a pair of these lenses
in my "Foldable"
picture showing typical detector sizes:
This is the "blur circle" of lens #3 (above) being
compared with the relative sizes of two sizes of
Click on the image for a larger version.
For comparison, Figure 16
shows the blur circle size of lens #3 (the "Page Magnifier"
and some typical detectors.
The larger square depicts the size of a BPW34 photodiode, a
diode that has an area of 7.5mm2
and is inexpensive
(well under $2 U.S. in small quantities)
and a reasonably good
performer in terms of leakage currents and intrinsic
noise. Its moderate size means that its capacitance is
quite reasonable (70pF at 0 volts, 25pF at 3 volts and just 10pF
at 20 volts of reverse bias)
and is large enough to be able to
"capture" pretty much all of the of light focused by the lenses
described on this page.
Also represented is the relative size of a hypothetical 1mm
diameter photodiode. A diode of this size has about 1/10th
the area of a BPW34 which will have comparatively lower
capacitance (because of its lower area)
as well as lower
intrinsic noise and such a diode would be capable of capturing
the vast majority of the light focused by this lens. Even
though some of the light would "spill" past a diode of this
size, it's likely that, compared to the BPW34, one would achieve
somewhat higher performance with it owing to the lower
capacitance of the diode and lower noise contribution. If
other light sources are nearby, the narrower field of view of
this diode/lens combination (as compared with the same lens
using the BPW34)
may provide additional performance gain by
helping reject off-axis sources that might otherwise "dilute"
the desired signals.
It's rather difficult to estimate the size of the "blur circles"
of the lenses tested above but it is very clear that the blur
circles are very much larger
than would be the airy discs
at the tested wavelength, but let's take another look at the Figure 16
where we are
testing lens #3. By inspection and "guesstimation" we'll
declare that the diameter of the blur circle (where the vast
majority of the spot is contained)
is, in round numbers, on the
order of 0.2mm. In looking at Table 1 (above)
we see that for an F-number of
1.25 (very close to the measured F-number of this lens)
diameter of the airy disc would be just under 1/1000th
of a millimeter - approximately a 200-fold difference!
So, we can see that neither this Fresnel lens - or any of the
others on this page - come anywhere
near the the
As a rough estimate and as a rule of thumb, the
diameter of the "blur circle" of a good quality, molded
plastic Fresnel lens is approximatly 1/1000th of the focal
length of the lens. It has also been observed that
some very high-quality lenses have 1/2-1/3 this size of blur
Implications for "transmitting":
Given that the area of a typical, high-power LED (such as one of
the members of the Luxeon or Cree family)
are at least 1mm2
in size, we can be reasonably assured that, for the majority of
the lenses described above (particularly those that have an
F-number below about 1.5)
that even after a moderate amount of
source-size magnification by a secondary lens, the divergence of
the resulting collimated beam will be largely set by the size of
the emitter and not
the quality of the lens.
Given a "typical", inexpensive Fresnel lens of "Page Magnifier"
size with a 300mm focal length, knowing the size of the "blur
circle" for such a lens implies that with a small emitter (that
is, one that is about the same size as the blur circle)
could achieve somewhere in the general area of 0.05 degrees
(about 0.9 milliradians)
of beam divergence. Considering
that the brightest LEDs (e,g, that is, those that have the
highest "current density" - number of amps per square millimeter
and thus the highest photonic density)
are much larger
than the blur circle, achieving that degree of divergence is
unlikely - unless one were to mask off
emitter and "throw away" the extra light!
The penalty of using a "larger than necessary" emitter is mostly
one of inconvenience in that more power is required to light up
the "unused" portion of the LED's emitting area, plus the fact
that the actual beamwidth tends to be broader - which has
implications when it comes to using a full-duplex optical
communications system and Rayleigh scattering increasing
transmit-receive crosstalk. On the positive side, a
broader beam makes aiming much easier and relaxes the mechanical
precision requirements of the emitter/lens assembly!
Implications for detectors:
As with the emitter, a detector of 1mm diameter (or larger)
more than adequate to intercept the vast majority of energy
being focused by the lens tested above to its focal plane.
Detectors much smaller than this (depending on the lens, of
run the risk of not
intercepting as much of the
distant source's energy, resulting in loss of efficiency.
The use of a detector that is much larger than the blur circle
could introduce inefficiency due to the capacitance and noise of
the photodiode degrading the signal from it as well as the
larger size increasing the field of view of the system.
All of this assumes that the detector is situated precisely at
the focal plane of the lens and that it can be held there
with good accuracy, despite transportation and handling!
With these (or any!)
lenses it is important that sub-millimeter
accuracy and stability be maintained in the structures in order
to keep the components in proper focus and paraxial alignment!
Hopefully, this page gives a general idea of what can be
expected from typical, molded plastic Fresnel lenses.
Again, this information can be useful in determining reasonable
sizes of detectors - or, as in the case of a Photomultiplier
tube which has a much
area", a reasonable size of aperture that might located at the
focal plane to limit the field of view. This information
also gives an idea as to what might be the limiting factor when
it comes to minimizing divergence for this type of Fresnel lens
- that is, lens accuracy/quality or the apparent size of the
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free to contact me using the information at this URL.
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