Winlens lab instructions

WinLens
Lens design and analysis
Computer lab Optics IO 2651,
IO 2692
Nicolas Innocenti
njain@kth.se --- 08 790 6271
Office: 163:007, Albanova Univsersity Centrum, Roslagstullsbacken 35
Based on lab manual by Per Martinsson

Introduction
In this computer laboratory, you will design and analyze a few different optical
systems using the software WinLens Basic.
Working on your own computer
The computer lab is performed on your own computer. You can download and
install the software (WinLens Basic) and the Lens Library on your own
computer from http://www.winlens.de/, and do the assignments on you own
computer. You need to install
• WinLens Basic, http://www.winlens.de/index.php?id=25
• WinLens Library 2002, http://www.winlens.de/index.php?id=68
Please do not hesitate to contact the teaching assistant if you have any problems
installing the software.
Working with other software
If you are familiar with (and have access to) other lens design software, such as
OSLO or Zemax, you can to do the assignments using your favorite lens design
software. However, the teaching assistant may not be able to answer questions
regarding the specifics of the software.
Optional Computer lab sessions
One or two computer lab sessions can be organized during weeks 43 and 44
(October 22 nd – Nov 2 nd ) upon request from the students. During those sessions,
the teaching assistant will answer questions and assist you in the use of the
software on your personal laptops.
Requests for sessions need to be sent to the teaching assistant by October
26 th latest, preferably in groups and with all possible time slots for the
session (plan about 4 hours/session).
The lab report
In order to receive credits for the lab assignment you must hand in a lab report.
The lab report should include answers to the questions in the lab instructions,
motivations for choices you have made, results and (brief) conclusions for the
different assignments. You are encouraged to report your results in the form of
graphs, tables and lens drawings from WinLens, when possible. (To copy the
screen to the clipboard, press SHIFT-PrntScrn. You can then paste a snapshot of
the screen into Paint, or a similar application. To copy individual graphs or
tables, right click on the graph/table and choose Copy graph/table to clipboard.)
If you do to the computer lab together with other students (co-operation is
encouraged), you only need to hand in one report per group.
The lab needs to be submitted by e-mail to the teaching assistant by Monday
November 5 th , 8.59 AM at the latest. Use PDF format and include
[Winlens2012] in the subject of the e-mail.

Please note that the teaching assistant will send a confirmation e-mail upon
reception of your report. If you don’t receive the confirmation within ~24
hours, send the report once again!
If you need help
If you have any questions regarding the lab assignment, or the installation of the
software, please do not hesitate to contact the teaching assistant. You find the e-
mail address, telephone number, and room number on the front page of this
document.
‘Major’ issues should be kept for computer lab sessions when possible.
Remark about the lab notes
The present lab manual was originally written for Winlens Free 4.4. You will
likely notice a few minor differences between the screenshots in the lab notes
and the interface in Winlens Basic. The usage principles of the software and its
functions however remain to a large extend identical.
Remark about the software
Some stability problems with Windows 7 64 bits have been reported. If you
face such problem, try running the software using “Windows XP Mode”
(Available for download at http://www.microsoft.com/windows/virtualpc/download.aspx
--- Short tutorial here:
http://www.sevenforums.com/tutorials/8247-windows-xp-mode-installsetup.html)

Getting started with WinLens 4.4
The purpose of this section is to get to know WinLens. You do not need to
include anything from this section in the lab report.
About LINOS Photonics WinLens 4.4
WinLens 4.4 is an optical design and analysis application that uses ray tracing to
calculate geometrical quantities, aberrations, optical performance etc. Using the
various menu options, spreadsheets and buttons, you can easily set and change
the parameters of the system, or otherwise modify the design.
Finding Help
WinLens has a good help system, with a well-structured table of contents. A
good way to get an overview of the functionality of the application is to browse
through the help files (starting from the table of contents). The help files include
a glossary of terms, where you can find explanations to important concepts of
geometrical optics. The help system is context sensitive, i.e. if you want help on
what you are currently doing, press F1 and the help page concerning your
current action (or more precisely, the currently active window) will be
displayed.
Getting started
Starting WinLens
You find WinLens on the Start menu under Start → All Programs → LINOS
Photonics → WinLens 4.4.
A note about decimal separator
Depending on the language settings for Windows on the computer you are using,
the decimal separator may be either a point or a comma. For instance, if you are
running WinLens on a Swedish version of Windows, you should use the comma
as separator. If you use the point it will be ignored, i.e. “3.5” is interpreted as
“35”.
The windows
When you start WinLens 4.4, two windows
• the System Data Editor (Fig. 1), and
• the System Parameter Editor (Fig. 2)
are displayed within the main window (“LINOS Photonics WinLens 4.4”).
These two windows are always displayed, you can not close them. The System
Data Editor is where you set up the lens system by adding parts to the
Component column. In the section “A user-defined lens” we will try this.

The System Parameter Editor has six tabs – Main, Conjugates, Aperture etc –
that you access by clicking the tabs. The System Parameter Editor is where you
set parameters such as wavelengths, field size, object distance etc.

The Windows menu
When you have many windows open, you may want to use the Windows menu
to find windows that have gone missing behind other windows. The System
Parameter Editor is always number 1 in the list, and the System Data Editor is
always number 2 – so you can access these from the keyboard by pressing Alt-
W-W-1 or Alt-W-W-2, respectively. The Tile Vertically option fills the
workspace with all open windows, and gives them equal sizes. You cannot undo
this, so if you have arranged the windows to a layout you like, don’t use this
option. The Cascade option puts the windows on top of each other, slightly
displaced so you can see all of them. Like Tile Vertically, Cascade cannot be
undone.
Adding a lens
A catalogue lens
In this section we set up a simple imaging system with one single lens and have
a look at some of its characteristics.
To open a catalogue of lenses with their respective design data,
• open the menu Data Base (ALT-D) and then choose Component Data
Base (SHIFT-C), or quicker: press F3 2
If you look at row 339 you will find an achromat, with focal length f=100mm,
and part no (NoMount) 322288000. If you don’t see it, click Full Database, and
it should appear. Click on the part no, and WinLens gives you a drawing of the
lens and informs you that the focal length is 100.04 mm at wavelength 587.6
nm, and that the diameter is 31.5 mm. To add the lens to your system,
• drag and drop the part no to the Component column in the System Data
Editor.
Now the lens is in place. (Typing the number into the Component column has
the same effect.) “Stop” on the same row as the lens means that the aperture stop
is immediately in front of the first surface of the lens.
The next step is to set the parameters of the imaging system. The System
Parameter Editor is where you do this. Look at the Main tab. Here you find,
among other things, the object distance. Its default value is –1000mm. To place
the object at infinity,
• change to the Conjugates tab and click the radio button Object at
Infinity.
To set the size of the aperture stop,
• go to the Aperture tab.
There, you find a number of different terms (NA, F/No etc) all describing the
size of the stop. If you are primarily interested in the flux of light through the
aperture, you should set the stop radius. To set the stop radius:
• click the Stop Rad radio button. Then enter the desired stop radius, say
5.0 mm, into the text box to the right of the radio button. Press Enter
and WinLens calculates the values for NA, F/No etc and fills in their values.

Now we need to set parameters for the object field.
• Select the Field tab.
• Select Object Angle and enter 10 (degrees). Press Enter.
WinLens now calculates the angle on the image side and the resulting image size
(radius) and displays their values (in this case the image has a radius of
17,665mm). If you would like a nicely formatted printout of all system
parameters, click the Show button on the Main tab and then click Print.
To display a drawing of the lens,
• select Lens Drawing in the Graphs menu (or click the icon with a lens
on it on the Graphs tab in the toolbar, or quicker: Press CTRL-D.).
The drawing contains the achromat, the stop (two red dots) and the chief ray
from the object point at 10 degrees from the optical axis.
To add more rays or other features to the drawing,
• right click on the drawing and select Select options for this drawing (or
press S). If you select the following features:
o Image Plane,
o Entrance Pupil [E],
o Exit Pupil [E’],
o Rear Focus [F’],
o Principal Plane 1 [P], and
o Principal Plane 2 [P’],
on the Paraxial features tab, and
o Paraxial Rays, and
o Extreme Rays in Fans,
on the Rays tab – you will have the lens drawing shown in Fig. 3.
Fig 4: Winlens’ drawing of lens with rays

A user-defined lens
Before you continue, remove the achromat:
• select the cell containing the part no (322288000), and press delete.
To create a lens,
• type “lens” in the Component column of the System Data Editor window
and then press Enter.
This gives you a spreadsheet (User defined lens: Component 1) where you can
enter lens radii, thickness, material, and aperture half diameter. First, create a
lens with the same data as that of the catalogue lens in the previous section. This
makes it easy to verify that you have got everything right. The lens data for the
catalogue lens can be found in the Surface by Surface table in Fig. 4.
The bi-convex first lens of the achromat has the radii 61.748 mm and –45.153
mm. The thickness (Sepn=separation between the surfaces) is 7.50 mm, and the
aperture half-diameter is 15.75 mm. Enter all these values into their respective
boxes. The material of the first lens is Shott N-BK7. Delete “air” from the Glass
box and type N-BK7, then press Enter, select glass maker Schott and click OK.
The negative meniscus lens has radii -45.153 mm (shared with the first lens) and
–130.04 mm. Its thickness is 2.00 mm and the lens material is N-SF5. When you
have entered all the data for the compound lens, press Enter. This gives you a
picture of the lens. The spreadsheet should now look as in Fig. 5. If it does, click
OK.

Now set the system parameters (object distance, aperture size, object angle) to
the same values you used in the previous section. Look at the Lens Drawing and
compare it to the one in Fig 3. It should look the same. If it does, you have
managed to create a lens using your “own” data!
More spreadsheets
Surface by Surface
To view the Surface by Surface table,
• click the Surf Data icon on the Tables tab on the toolbar.
You can see that your own lens gives the same Surface by Surface table as the
one in Fig. 4.
Pressing F1 (Help) tells you that this table is called Surface Data Table/Editor.
In other words, you can use this table as an editor to change surface parameters.
The parameters that can be changed have a yellow background. Try this; change
the first radius from 61.748 mm to 51.748 mm. The refractive power of the lens
increases and the back focal length decreases from 95.38 mm to 81.39 mm. You
can also see the difference in the lens drawing.
Undo
WinLens has an ”undo” option (Edit menu -Undo option, CTRL-Z, or this
icon). Undo takes the program back to the state it was in before the last change.
The undo-functionality in WinLens doesn’t hold a list of previous states. This
means that you can only change between the state after the latest change and the
state before the latest change. If you do undo several times, you switch between
these two states. Try this; after changing the radius to 51.748 mm, press CTRL-
Z. The radius is 61.748 mm again. Press CTRL-Z again and the radius changes

ack to 51.748 mm. This way you can switch between the two radii and observe
the difference in the lens drawing.
Paraxial values at mid wave
Paraxial values at mid wave gives you the values of all the important quantities
you find along the optical axis of the system. (“Mid wave” refers to the Mid
Wavelength that is set on the Waveband tab of the System Parameter Editor.)
To open this table,
• click Parax Sys on the Tables tab
Paraxial Data: Surfaces
Paraxial Data: Surfaces is the component level equivalent of the Paraxial
values at mid wave table.
To open Paraxial Data: Surfaces,
• click Parax Comp on the Tables tab
Paraxial Ray Trace
This table shows the ray tracing data in numbers. The height and angle of the
marginal and principal rays, at each surface through the whole system, are
displayed.
To open the Paraxial Ray Trace table,
• click Parax Rays on the Tables tab
Performance characteristics
Spot Diagrams and Geometric MTF
Spot Diagrams and Geometric MTF show the spreading (blurring) of object
points as they are reproduced in the image by the optical system, i.e. they give
you information on detail reproduction, resolution and sharpness.
Spot Diagrams
Spot Diagrams show where rays intersect the Gaussian image plane, as well as
planes in front of and behind the Gaussian image plane.
To view the spot diagrams,
• Click the Spot icon on the Graphs tab on the toolbar.
In Fig. 6 the spot diagrams show the intersection of the rays with planes located
at -2mm, -1mm, 0, 1mm and 2mm relative to the Gaussian image plane. The
distance between the planes can be set in the Spacing box above the spot
diagrams. You can also change the scale of the diagrams (in the Scale box). In
Fig. 6, there are two rows of diagrams. Each row corresponds to one object
point. With the parameters you entered in the section “A catalogue lens”, the top
row corresponds to the on-axis object point, and the bottom row corresponds to

the object point at 10 degrees from the optical axis.
The spot diagram shows a distribution of light around a point in the image. With
an infinite number of rays, the distribution would be the point spread function
(PSF). To get a good approximation of the PSF, you should make sure that you
use enough rays.
• Select Number of Ray Rings in the Options menu
• choose 15 rings.
WinLens can reduce the dots in the spot diagram to numerical values by
calculating the root mean square of the distances from the Gaussian image point
to the points where the rays intersect the plane. To see these r.m.s. distances,
• click the Summary button
Even a diffraction-limited system will reproduce a dot as a distribution (the Airy
disc); the radius of the Airy disc is given in the summary (look for Diffraction in
the Field column, and Spot Rad in the Data type column), so you can compare
the performance of your system to the physical limit.
The size of the Airy disc is also displayed in the spot diagrams, as a red circle,
when the Airy checkbox is checked. To see the Airy disc, make sure that the
scale is small enough.
• Close the summary
• Change the scale to 0.1 and press Enter
The red circle corresponding to the diffraction-limited spot size should now
appear in the spot diagrams.

Geometric MTF
The Modulation Transfer Function (MTF) is a measure of how contrast is
preserved in the imaging process. Modulation (or contrast) is defined as
Modulation = M = I !"# − I !"#
I !"# + I !"#
,
and the MTF is defined as the ratio of the image modulation to the object
modulation, i.e.
MTF = M !
M !
.
The object can be envisioned as a superposition of sinusoidal gratings of
different spatial frequencies. Each sinusoidal component is affected differently
by the imaging system (the image modulation deteriorates for high-frequency
components), and accordingly the MTF is a function of spatial frequency.
To view the Geometric MTF diagram
• click the MTF icon on the graphs tab
In this double diagram, which is shown in Fig. 7, you find on the left hand side
the MTF in the Gaussian (paraxial) image plane. The horizontal axis
corresponds to spatial frequency. The scale is set in the text box below the
graphs. WinLens, by default, sets the scale to the cut-off spatial frequency of a

diffraction-limited system 13
with the same numerical aperture as the current
system. As in the spot diagram, the rows of graphs correspond to the different
object points.
On the right hand side you find what WinLens calls the Thru MTF, i.e. the MTF
for a specific spatial frequency, in planes in front of and behind the Gaussian
image plane. The horizontal axis corresponds to the distance to the Gaussian
image plane, known as the defocus. In the Thru MTF diagrams, you can see in
which plane you have maximal focusing. For Thru MTF, WinLens uses the half
cut-off frequency by default – you have to choose a reasonable frequency
yourself - for instance 100 cyc/mm for a camera objective. For further
information on the MTF graphs, see Help (press F1).
Chromatic Aberration
Chromatic Abn: EFL/BFL displays the longitudinal chromatic aberration, i.e. the
focal length as a function of wavelength.
To open the Chromatic Abn graph,
• click the COL icon on the Graphs tab of the toolbar.
You can choose between effective focal length (EFL) and back focal length
(BFL). Numerical values are given for the five wavelengths that can be set on
the Waveband tab of the System Parameter Editor.
1 The cut off frequency of a diffraction limited system (where the MTF approaches zero) is

Field Aberrations and Transverse Ray Aberrations
Field Aberrations
To view the field aberrations
• click the FLD icon on the Graphs tab of the toolbar.
Field Aberrations displays three diagrams: Astigmatism, Distortion and Lat
Colour. In each diagram, the horizontal axis represents the aberration, and the
vertical axis represents the position in the image field. The highest point on the
vertical axis corresponds to the maximum value for the image field (the Image
Size Radius on the Field tab of the System Parameter Editor).
The Astigmatism is the difference in focus between the meridian and sagittal ray
fans. The horizontal axis of the Distortion graph represents the quantity
h − h′
h ,
where h’ is the distance from the optical axis to the chief ray, and h the distance
from the optical axis to the paraxial chief ray. The distances, h and h’, are
calculated at the image plane.
The Lat Colour graph shows the lateral chromatic aberration, i.e. the deviation,
calculated in the image plane, of the chief ray due to dispersion. See Fig. 8. The
deviation is calculated relative to the chief ray corresponding to the mid
wavelength.
Transverse Ray Aberrations
To view the transverse ray aberration graphs,
• click the TRA icon on the Graphs tab of the toolbar.
Transverse Ray Aberrations shows the displacement of a non-paraxial ray from

the chief ray originating in the same object point. The displacement is calculated
in the image plane. There are two graphs for each object point, one for the
sagittal ray and one for the meridional ray. The horizontal axis represents the
normalised aperture coordinate. A meridional ray (from an object point below
the optical axis) going through the lower edge of the aperture has its aperture
coordinate at the leftmost point of the horizontal axis. The vertical scale shows
how much higher the ray intersects the image plane, compared to the chief ray.
By reason of symmetry, the sagittal ray fan aberrations are the same on either
side of the aperture, so only one half is plotted. For further information, see Help
(F1).
Seidel Aberrations
Seidel Abberations (icon SEIDEL ABNS, tab Tables) will only be briefly
commented here: For a wavefront to converge to a point, it has to leave the exit
pupil as a sphere whose center is the image point, known as the Gaussian
reference sphere. In 1856, Ludwig Seidel derived an expression for the
difference between the true wave front and the Gaussian reference sphere. (The
“true” wavefront in this context is the wavefront as described by third order
theory.) He found that the difference can be expressed as a polynomial of five
terms, containing different powers of the image field angle, the aperture radius
and the azimuth angle of the ray fan. Each of these five terms relate to one of the
aberrations: spherical aberration, coma, astigmatism, curvature of field, and
distortion. Every surface in an optical system introduces wavefront aberrations.
These add up on the way through the system, and the aim of the designer is to
make the sum of the aberrations as small as possible. The quantitative relations
between the Seidel aberrations and the ray aberrations require a lot of
mathematics, but we can use the Seidel Aberrations table to look at the sums for
each aberration (in the first row of the table – Totals), and to see the contribution
of each surface of the system to the total aberrations. We can, for instance, see
how we through “lens bending” (the redistribution of refractive power between
the surfaces) can reduce the spherical aberration. See also the help files (“Seidel
Aberration Table”, “Seidel Aberrations”, “Wavefront Aberration Polynomial”).

Simulation, design, and analysis of
simple optical systems with LINOS
Photonics WinLens 4.3
This section is the actual lab assignment.
1. Lenses and some characteristics
General comments
In this part of the assignment you will set up a simple convex planar lens and
analyze its performance using the criteria you find appropriate. You will also
compare it to an achromat from the component database. An achromat is a lens
(most commonly a doublet lens) designed to limit the effects of chromatic and
spherical aberration. Suggestions of graphs and tables to analyze are
o Spot Diagram
o Spot Diagram Summary
o MTF
o Transverse Ray Aberrations
o Field Aberrations
o Chromatic Aberration
o Seidel Aberrations
To achieve good accuracy for spot diagrams and MTF, always use 15 Ray Rings.
(You set the number of ray rings on the Options menu).
Use screen printouts or screen snapshots, with your own comments, for your lab
report. To copy the screen to the clipboard, press SHIFT-PrintScrn. To copy
individual graphs or tables, right-click the graph or table and click Copy
graph/table to clipboard.
Tasks
Typing “lens” in the Component column of the System Data Editor, set up a
simple planar convex lens with focal length approximately f=100 mm, aperture
diameter > 30 mm, and glass type Schott BK7 (having refractive index n=1.52).
a) Set the following system parameters
o Object Distance = infinity (the Conjugates tab of the System
Parameter Editor)
o Stop Radius = 10 mm (Aperture tab)
o Object Angles 0 and 10 deg (Field tab)

Compare and discuss the imaging performance of the lens, and its most
important aberration(s), for
a. The planar side of the lens towards the object
b. The convex side of the lens towards the object (Fig. 1 illustrates how
to change the orientation of the lens)
b) Choose the better orientation of the two above and reduce the Stop Radius to 5
mm. What do you gain, in terms of imaging performance? What is the trade-off,
i.e. try to think of what you loose by reducing the stop radius. (It is not in any of
the tables or diagrams in WinLens.)
c) Use the catalogued achromat with part no. 322288000 (drag and drop the part no.
from the component database, or type it directly into the Component column of
the System Data Editor). Discuss the differences of its performance to that of
your simple lens.
2. Six-lens objective
General comments
In this task you should analyze a six-lens objective, how it is affected by a
planar filter, and how it performs at short object distances. To analyze the
system, use
o Geometric MTF
o Chromatic Aberration (COL)
o Field Aberrations (FLD).
Tasks
Load the six-lens objective for a small-image camera 1.8/50 mm of double gauss
type. You find it under \LIBRARY\Double_Gauss_Lenses\wldg014.spd in the
folder where you extracted the ZIP containing the library download from
WinLens’ website. Reduce the aperture size - set F/number to 4 (on the Aperture
tab of the System Parameter Editor). Set the object angle to 10 deg (on the Field
tab of the System Parameter Editor).

With the object at infinity, register the Geometric MTF, Chromatic Aberration
(COL) and Field Aberrations (FLD).
a) The effect of a filter on the quality of the image
In photography, filters are used for many different purposes. In this part of the
exercise, you will examine the effect of the filter on the quality of the image.
The exercise does not concern the actual filtering effect (color correction,
polarization etc), only the effect on the image due to refraction at the filter
surfaces. For this reason the “filter” is modelled as a simple glass plate. To make
the effect visible, use a rather thick filter: a planar parallel plate of BK7, 20mm
thick, and 50mm in diameter. Create the filter as a user defined lens with infinite
radius of curvature for both surfaces. To achieve infinite radius of curvature, set
the radius to 0. Place the “filter”
a. on the image side, immediately behind the objective
b. on the object side, immediately in front of the objective. (Use the
Insert Blank Row option on the Edit menu to make room for the filter in the
system data editor.)
Compare the Geometric MTF, Chromatic Aberration and Field Aberrations for
the three cases
o No filter
o Filter behind the objective
o Filter in front of the objective
Discuss what happens when a planar parallel component (the filter) is added to
the optical system. (Feel free to use additional characteristics for your analysis.)
Draw conclusions and make a recommendation regarding where to place the
filter.
b) The effect of object distance on the imaging performance
Most camera objectives are designed to give their best image formation for
distances of 100 focal lengths or more (i.e. image distances approximately equal
to the focal length). We will now change parameters to analyse what happens
when we use the objective for
1:1 imaging.
Remove the filter. Then do a and b below.

a. Choose (on the Conjugates tab) Finite conjugates and Magnification = -1.
Compare the performance (primarily using MTF) with the performance you saw
with the object at infinity. You should see a dramatic loss in performance.
b. Now put the achromat 322288000 in front of the objective, and look at the
image quality at 1:1 imaging for the combination of the achromat and the
objective. Compare the results to 1:1 imaging without the achromat.
Analyse and comment the results.
3. Optical connector for fiber communication
Design a connector for optical fibers. The connector should be of the type
illustrated in Fig. 2 below. Don’t include the fibers in your design – instead let
the object be the end of one fiber and the image the end of the other fiber. Use
one single object point on the optical axis. For the connector, use a pair of glass
spheres with 4 mm diameter. Use glass
Fig 2. Optical fibre connector
the spheres be 2 mm. Put a stop, with 2 mm diameter, between the spheres. Set
the wavelength to 850 nm, i.e.
• go to the Waveband tab of the System Parameter Editor. Enter a value
larger than 850 in the Long Wavelength and the Long Wavelength 2
textboxes. Then enter 850 in the Mid Wavelength text box.
• set the number of wavelengths, on the Options menu, to 1

The fiber ends should be very close to the spheres, in other words, let the object
distance be small (fractions of a millimetre). Your objective is to maximize the
coupling efficiency by imaging the end of the first fiber onto the end of the
second fiber. Due to spherical aberration, the image spot in the Gaussian image
plane is large. Reduce the size of the spot by compensating as much as possible
with defocus on the image side. (You find Defocus on the Options menu.) Check
the result with Spot Diagram and Spot Diagram Summary.
Report your results, with your own comments, a printout or snapshot of the
System Parameters, and a printout or snapshot of the screen containing at least
o
o
o
o
Main Parameters
Lens Drawing
Paraxial Values at mid wave
Surface by Surface.
4. Reverse engineering
In this exercise you are going to design the optics of the simplest of all cameras,
a disposable one-lens camera. You can find the information you need from the
pictures below.
Before continuing, make sure to restore the wavelengths to visible light. You
can find default settings for visible light in the Default Wavebands dropdown list
on the Waveband tab of the System Parameter Editor.
In Figs. 3, 4 and 5, the lens of the camera is shown. Make an estimate of the lens
diameter and the radius of curvature of the convex surface of the lens. The
estimates do not have to be accurate - they are merely intended as a starting
point for you to optimize from. As can be seen from the pictures, the lens is of
the meniscus type. The radius of curvature of the concave surface is difficult to
estimate, but it has to be larger than that of the convex surface. (Otherwise, the
lens is negative, and will not form a real image.)

To make it easier to compare different solutions we will make a few
assumptions. We assume that the focal length is 35 mm and the f/number is 11.
The lens is to be made of Plexi-Glass (polymethylmetacrylate PMMA). This
leaves the following variables for your optimization:
o the two radii of the lens
o the thickness of the lens
o the position of the aperture stop
o the position of the image plane relative to paraxial focus on the axis
o the curvature of the image plane
PMMA is not in the WinLens materials database. You can create a temporary
material by typing PMMA in the Glass column of the spreadsheet for the user
defined lens, and then pressing Enter. A dialog box appears. Choose Select index
data from n1, V and enter the values n = 1.491, and V = 57.2. If you make a
mistake, you can not edit the data for the temporary material PMMA. Instead,
create another temporary material, e.g. PMMA2, with the correct data.
In most disposable cameras, the aperture stop is positioned immediately behind
the lens, as in Fig. 6. You can choose to position it elsewhere, but keep in mind
that the image distortion generally increases with the distance from the aperture
stop to the lens.

From Fig. 7, you can get an idea of what the curvature of the image plane is for
a disposable camera.

This camera has no mechanism for adjusting the focus, so we choose 4 m as
fixed focus distance.
Let WinLens use three points for its calculations: the axis, the long side of the
negative (r=18 mm) and a third point in between.
A planar object normal to the optical axis, imaged by a simple lens, will be
imaged as a plane only approximately. The image field is actually curved. To
compensate for this curvature, we will bend the film. Let the curvature of the
image plane be spherical, and only consider the meridional plane, ignoring that
the film in practice only can be cylindrically bent. The radius of curvature of the
film (i.e., of the image field) cannot be arbitrarily small, so you have to choose
parameters that give you a reasonable field curvature. See the hint on field
curvature below.
Analyse the spot diagrams and try to optimize the spot-sizes. Don’t forget to
consider the off-axis points.
Analyse the MTF. The 24x36 mm 2 negatives are usually enlarged to 10x15 cm 2
paper copies, i.e. approximately 4 times. When observing paper copies the
perceived sharpness is correlated to the MTF of the image at approximately 2
cycles/mm. Therefore, optimize the MTF for the spatial frequency 7.5 cyc/mm
in the image plane.
To analyse the depth of focus of your camera, investigate its performance at
object distances ∞ and 1 m. At 1 m, the camera is defocused and you have to use
defocus to achieve good imaging.
Report your considerations and results, specifically the values you choose for
the six design parameters. Make sure to report all relevant data. (You can, for
instance, report your parameter values in form of a screen printout or snapshot
as in Fig. 8)
Hint about field curvature
Neglecting astigmatism, the displacement Δx of an image point from the
paraxial image plane is given by (the Petzval curvature)
∆x = y!
2
!
R !
1
n ! ′ − 1 n !
,
where y is the height in the image plane, Ri is the radius of curvature of the i:th
surface, and ni and ni’ are the refractive indices in front of and behind the i:th
surface, respectively. For a simple meniscus lens as those in the disposable
cameras,
∆x = y!
2 R ! − R ! 1 − 1 n !
,

where n i is the refractive index of the lens, so to reduce image curvature, the
radii of curvature should be chosen so that R2 – R1 is small. Because the focal
length is fixed, this means that the radii of curvature have to be small. This
causes strong spherical aberration, so there is a trade-off between field curvature
and spherical aberration. Remember that spherical aberration can be reduced by
proper placement of the stop.