Lens design: then (1964) and now (1996) by Bruce H. Walker
O ,F]\ v`[Tl Much has been said and written about the changes to the lens design process over the recent decades. Having worked in this field for the past 30+ years, I have enjoyed being involved with many of those changes. This paper will share some general observations on the subject, and then quantify the impact of those changes by review of a specific lens design first executed in 1964 and then updated in 1996 by application of today's technology.
c,#~L7 ^4xlZouCb The lens design process
p56KS5duI. Typically, the lens design process begins with a set of
optical specifications describing a lens that must meet an established set of performance criteria. Next, the lens designer calls upon personal experience, along with that of others, to identify an existing lens form that has the potential of meeting those specifications with a minimum of modification. This starting lens form is then manipulated by the lens designer, in an effort to make it conform to the established optical specifications. Key to this lens optimization stage are the tools used by the lens designer in the process. Typically, there are three basic tools involved: the computer (hardware), the lens design program (software), and the skill of the designer. All three are essentialno one is more important than the others. The final phase of the lens design process is the unambiguous documentation of the final lens prescription (suitable for manufacture), and of the optical performance that can be expected of the final design.
5 {T9* b aUEsg[~V Hardware and software
?$"x^=te7 While the experience and skill of the lens designer is difficult to quantify, improvements in hardware and software over the past 30 years have been vast, and are easily identified. Each lens designer who has worked in the field during these years has followed a path somewhat different from that of his or her colleagues. While typical may not be the best term, I believe my experience accurately reflects many of the changes that have occurred during this time period. Prior to establishing an engineering consulting business in 1991, I had worked for three companies, each involved in a unique aspect of the
optics industry. Initially my lens design work was accomplished using a small (that meant it all fit into the same room) IBM-1620 computer, with a rudimentary software package provided by the computer manufacturer Later, I would work using a computer terminal, connected via phone lines, time sharing a large remote computer, with an optical design software package (ACCOS) installed on that computer. Around 1980 this changed to an arrangement where an in-house minicomputer was available, to be used with a leased software package (CODE IV). Today, I work with a Pentium PC, and have installed on that computer a reasonably priced lens design and optical engineering software package1, which meets all of my optical engineering and lens design requirements.
RZ#alFL, ?~VWW<lR l>3M|js@/ While attempts at cost and speed of computing comparisons are possible, I feel they have lost much of their relevance in recent years. Suffice it to say that the speed with which calculations are now executed far outstrips the designers ability to keep up with the volume of useful data output. Likewise with cost of computing, the speed with which solutions and data are generated, the bargain prices of today's hardware, and the cost of today's typical optical design software package, make the overall cost of computing (in most cases) trivial when compared with the fees being earned by the competent optical designer. Hats off to everyone involved in bringing about this spectacular revolution. Not only have they made all of us better designers and engineers, they have made our lives and work easier and a lot more fun.
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L A typical example
l fU"SSQ I would like to illustrate a few of the changes that have occurred over the past 30 years by taking a single lens design, one that I was responsible for in 1964, and describing how that design was generated. Recently, I have restored this design, evaluated its image quality, and examined the potential for its improvement by application of today's tools and techniques.
Z^/z H MEs8. Early in 1964 I was presented with a request for a lens design that would meet the following specifications:
gmF_~"^34 htUy2v#V Effective focal length (EFL): 260 mm
H{ n>KZ]\ Aperture: f/3.0
&y#\1K Image size: 25-mm dia. (5.5-deg field-of-view)
_Ewy^;S%L Wavelength: 1.06 µm (laser energy)
! # ,- Overall length (First surface to image): 260 mm
B|]t\(~$ [ Resolution: > 25 line pairs/mm
X7XCZSh#A The aperture and field specifications indicated the need for a lens form generally referred to as the Petzval type. This form contains two widely spaced lens groups, with the distance to the image plane (back focus) equal to about one half the lens group separation. In order for the overall length to be approximately equal to the EFL, it is required that essentially all of the lens power be contained in the first lens group, while the second group has zero net power, but is used only to correct aberrations. A starting lens form with three elements in the first group and two in the second was chosen as a starting point for the design process.
[M7iJcwt p z*/4 The basic approach used was to first, optimize image quality on a curved surface, and then to add a field flattener lens as a final step. Being a single wavelength design, the choice of glass types was less critical than is generally the case. It was important to select a glass type that would be compatible with handling of laser energy. This glass would need to be essentially free from strafe, bubbles and surface blemishes.
Jf %!I d vg; Rather than working with exact ray trace data, the optical design software in use at that time would only permit the correction of 3rd order aberration coefficients during the optimization process. Two of the lens curvatures were used to maintain the lens power distribution between the two lens groups. The remaining (eight) lens curvatures, along with the curvature of the image surface, were used as variables during optimization.
mr{k>Un\ ++J Bbuzj! Spherical aberration, coma, distortion and astigmatism were the aberrations controlled during optimization. It was found that a balance between third and fifth order spherical and focus would result in satisfactory on-axis performance. Coma and astigmatism were controlled to produce the best possible off-axis performance. Toward the end of the optimization process, a piano concave field flattening lens was added very close to the image plane to yield the final lens design (Figure 1a).
hQg,#r(JE4 ~c O?S2!W +Bt LyQ %KabyvOl) /?.r!Cp Figure 1. Original 6-element, 260-mm, f/3.0 lens design, generated in 1964.
mC{!8WC@k dyQ<UT /ctaAQDUh\ qHC*$v#.V? Figure 1b.
c"f-$^< The simplified, improved, 5-element f/2.12 design, generated in 1996 (right). All figure designs by Bruce H. Walker.
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Evaluation of image quality for the optimized lens form was accomplished by calculation of ray aberration curves, spot diagrams and encircled energy. This analysis indicated that the lens would produce a spot with a radius of about 0.005 millimeters. The lens specification called for a resolution that would be greater than 25 line pairs (cycles) per millimeter. This frequency can be represented by a series of black and white stripes at the image plane with individual widths of 0.020 mm. Since the spot radius was considerably less than the space between stripes, it was concluded that the blurring of the 25 line pair image by this lens would not be of such magnitude as to make the image unresolvable. Based on this analysis, the design was deemed acceptable, documented and released for manufacture. Testing of the prototype lens assembly verified the validity of the design.
^-e3=& )9A<fwpN An analysis update
a>)_ `m Recently, the original 1964 design was resurrected and loaded into my computer system for analysis. Aberration and spot diagram data were first generated to confirm the initial design and analysis (see Figures 2a and 3a). Analysis of the design was then expanded to include more modern methods. The modulation transfer function (
MTF) was generated to give an indication of the image contrast at the target frequency of 25 cycles per mm. While initial conclusions had been that this frequency would be easily resolved, this new MTF data indicated an on-axis image contrast of about 0.80indicative of very good image quality (Figure 4a).
{|Mxvp*Hg k$$S!qi# X*0eN3o. &;NNU T>Q J]=aI>Ow l(k rUv Figure 4. Modulation Transfer Function (MTF) curves for the original 6-element f/3.0 lens design (1964).
,z0~mN UijuJ(Tle y0&V$uv/ 3I U$ Corresponding MTF curves for the simplified, improved, 5-element f/2.12 design. Note the overall increased modulation, along with greatly improved consistency over the field (1966).
d FI.`pB Finally, using the "extended source" routine, it was possible to generate a graphic representation of the image that would be formed by this lens of a 3-bar resolution target with a frequency of 25 cycles per millimeter at the image plane. That simulated 3-bar image (Figure 5a) confirms earlier conclusions regarding the ability of this lens design to clearly resolve the specified frequency over the full field of view.
@ 2%.>0s. AXNszS%4 PoBu kOv k"DQbUy0L 7b 7% ( U'sVs2sk6 XDrlJvrPL Figure 5(a). Image plots. Simulated images of a 3-bar target with a frequency of 25 cycles per millimeter (at the image plane) as formed by the original 6-element f/3.0 lens design. Image on the top represents the on-axis case, on the bottom the maximum field point.
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@3)D%h Q8gdI _ Sk< S \DcC1W %T ,\xZ Figure 5(b). Image plots. Simulated images of a 3-bar target with a frequency of 25 cycles per millimeter (at the image plane) as formed by the simplified, improved 5-element f/2.12 lens design. Image on the top represents the on-axis case, on the bottom the maximum field point.
X."h Tha5 #/XK&(X Potential for improvement
I).^,%>Z) To assess improvements that have occurred in the area of lens design optimization since 1964, the original design was then reoptimized using modern software. Rather than working with aberration coefficients, today's typical optimization routine allows the tracing of exact rays, and the reduction of the spot size formed by the lens at several field points simultaneously. It was noted from Figure 1a that the original design contained two similar negative lenses as the last two elements. It seemed reasonable to assume that they might be combined into a single element. This move would not only eliminate one element from the design, it would move the final element a substantial distance from the image plane. Elements that are close to an image plane tend to cause problems, in that any surface blemishes on those elements will be nearly in focus and will tend to degrade final image quality. Also, these elements tend to physically interfere with other hardware, such as shutters or filters that may be located close to the image plane.
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IX[ This simplified form was introduced into the optimization routine with the same constraints (EFL, f-number, field of view, and overall length) that had applied during the original optimization phase in 1964. It became apparent early on that a lens with vastly improved image quality could be achieved. While the original design had exhibited wavefront errors of 1/4 wave on axis and 1 wave at the edge of the field, the reoptimized design was found to have wavefront errors that were less than 1/10 wave over the entire field. These results indicate the potential for improving on one or more of the lenses's basic characteristics. It was decided to modify the design, with the goal of increasing its aperture while maintaining essentially diffraction limited (1/4 wave) performance over the full field of view. After a few trial runs it was concluded that a goal of doubling the amount of energy collected by the lens would be reasonable. Since the original design had an f-number of f/3.0, the energy collected will be doubled when that f-number is increased to: f/3.0 divided by 1.414 = f/2.12. For the design EFL of 260 mm, this increases the entrance pupil diameter of the lens from 86.7 mm, to 122.6 mm. The simplified lens form was optimized with this increased aperture. The resulting lens is shown in Figure 1b.
d9[6kQ] {Gb)Et]< zM8/ s96h Performance comparisons
<2TB9]2. g The new (f/2.12) design was then evaluated using the same methods that had been applied to the original design. Examining the aberration curves in Figure 2b,
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Vt& 3$kv%uf{ Me K\eZ\ (W }i287 Figure 2a. Ray trace analysis of the original 6-element, 260-mm, f/3.0 lens design.
PU@U @ M*T# 5 v0jz)z<# Corresponding data for the simplified, improved, 5-element f/2.12 design. Note that the vertical scale on the left is 0.05 mm, on the right it is 0.01 mm.
I8-&.RE it can be seen that, in addition to a general reduction in amplitude of the aberrations (note the 5?change of scale), the uniformity of the curves for all field points has been dramatically improved in the new design.
v;F+fOo /J9T=N Looking at the spot diagram data for the original design in Figure 3a,
9V4V}[% a,0o{* (u$ ;ijfI P+zI9~N[ nE " b` Figure 3a. Spot diagrams for the original 6-element, 260-mm, f/3.0 lens design.
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}~\].I6 woH3?zR {If2[4!z Figure 3b. Corresponding spot diagrams for the simplified, improved, 5-element f/2.12 design . Note the overall reduction in spot size, along with greatly improved consistency over the field.
-Bwu$$0 it can be seen that the spot radius ranges from 0.005 to 0.008 millimeters as we go from the center of the image (on-axis), to the edge of the field. In the new design that spot radius has been reduced to about 0.003 millimeters for all field positions.
z_,] fd=o -I$txa/"| The MTF data for the original design (Figure 4a) shows that the on-axis image modulation is 0.8 at a frequency of 25 cycles/mm. For the maximum field position the modulation at 25 cycles/mm falls to less than 0.7. Note that the 駃deal,?or maximum possible modulation for this lens, due to diffraction limitations, is about 0.9. In Figure 4b it can be seen that the corresponding diffraction limited modulation for the new design has been increased to 0.93 due to the increased aperture. The contrast at 25 cycles/mm for the new design falls between 0.90 on-axis and 0.87 at the maximum field point. This indicates not only an improvement in general image quality, but a significantly improved uniformity of image quality over the entire field of view.
<GFB'`L 4Igs\x{i Finally, using the extended source routine, a simulated 3-bar pattern at the frequency of interest (25 cycles/mm) was generated for the original design and the new design for both the on-axis case, and for the maximum field point. The results are shown in Figures 5a and 5b, clearly illustrating the improvement in image quality and uniformity of image quality that has been realized.
5@&i:vs5y @Ozf}}# .pu`\BW> Conclusions
T=p}By3a The brief study described here demonstrates the fact that the tools of the lens design trade available today offer the potential for producing lens designs that are simpler, have improved basic parameters, and deliver significantly improved image quality, as compared to designs generated 30 years ago. The new design generated and described here is probably close to the ultimate design possible for this lens form and these specifications. It is quite probable that in another 30 years this design will be reexamined and found to come up seriously short of contemporary standards. That phase of the study will be left to the next generation of optical design engineers.
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<< Bruce H. Walker is the author of Optical Engineering Fundamentals, an optics textbook published by McGraw-Hill, and numerous articles dealing with the subjects of optical engineering and lens design. He is an independent consultant. Contact him at Walker Associates, 29 Pomeroy Meadow Rd., Southampton, MA 01073. Phone: 413/527-6552. Fax: 413/527-5436.
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6* A'AWuj\r2R Reference:
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OSLO PRO v5.1 from Sinclair Optics.
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,(9 _# http://www.spie.org/app/Publications/magazines/oerarchive/june/jun97/lens.html
