The revolution and design of photographic lens with zemax

Flowchart diagram photographic lens review several classic lenses redesign with zemax analyzes propertiesoptic theories and methods Cooke Triplet lens analyze description pre-calculation

中 華 民 國 一 百 零 五 年 六 月

Acknowledgement

This thesis does not just reflect the works done at the Opto-electronic System

Design Laboratory-Feng Chia University including many project experiences, but it

also represents a personally enriching and unforgettable time in Taichung, Taiwan

Firstly, I would like to thank to Feng Chia University for giving me scholarship

to complete my education

My deepest appreciation goes to my advisor Professor 李企桓 (Chi-Hung Lee)

for accepting me as his student He has provided me the valuable information and

suggestions for my research

My gratitude goes to all the lecturers who have taught me and staffs in

Department of Electrical Engineering for their friendly support Their useful

comments and suggestions improved the quality and contents of this research

Thanks also go to all my lab-mate who are very kind and give me supports

enthusiastically They were and are helping me to solve many problem in learning as

well as in other fields

Especially, I want to thank to my parent, my relatives for their continuous and

unquestioning support of my study It is more than the moral support and constant

encouragement

Dang Xuan Du 杜光東 電機工程學系碩士班

Abstract

Before the breakthrough of photography, pictures were rare and exclusive All portrait

or landscape picture was created by the oblique way, the ingenious hands But with the invention of lens, a little piece of glass that would change the world The lens started a formidable revolution in our ability to explore our surroundings, increase our knowledge, and gradually made it possible to alter our circumstances in a positive way Since the invention of lens, it has been undergone many revolutions that was in ordered

to satisfy the needs and requirements on its own time

Each of new type of lens was invented to solve the drawbacks of the previous lens, then improve the quality and performance So, in chapter two, we are going to redesign some

of these important lenses by Zemax, analyze their properties, estimate their quality to have a clearer understanding in the development progress of lens Consequently, a series

of lens has been designed and shown up already

In the next chapter, the discussion about related optic theories that useful for optical design The methods were used to do the works in this study also mentioned By combination between the own optical knowledge, design skills, applying new technology and the powerful of software, the lens has approached a good quality of performance

Tessar lens and Cooke Triplet lens were the two outstanding lens and were widely used

in many applications, so a research and design new versions of these lens will be the main tasks in this study

Keywords: Photographic lens, Cooke Triplet lens, Tessar lens, history of lens

CONTENTS

Chapter 1: INTRODUCTION 1

1.1 Review of photographic lens 1

1.2 The aim and objectives in the study 2

CHAPTER 2 LITERATURE REVIEW 4

2.1 Landscape lenses 5

2.2 Achromatic landscape lens 6

2.3 The Petzval Portrait lens 8

2.3.1 Rapid Rectilinear lens 10

2.4 The Cooke lens 11

2.5 The Celor lens 13

2.6 The Tessar lens 15

CHAPTER 3 USEFUL OPTIC THEORIES AND METHODS 17

3.1 Useful optic theories 17

3.1.1 The derivation of primary axial color equation 17

3.1.2 Field curvature flattening 20

3.1.3 Power equation for multiple elements optical system 21

3.1.4 Celor equation derivation and apply for Cooke triplet design 23

3.2 Methods 25

3.2.1 Cooke Triplet lens and specifications 25

3.2.2 How to select the glasses 26

3.2.3 Design procedure of Cooke triplet 28

3.2.4 Tessar lens and specification 32

CHAPTER 4 RESULTS 35

4.1 The Cooke Triplet lens 35

4.1.1 The progression 35

4.1.2 Final results and comparison 42

4.2 Tessar lens f/2.8, 52mm 48

4.2.1 Lens data 48

4.2.2 System descriptions 49

4.2.3 Layout of lens 50

4.2.4 Ray fan plots 51

4.2.5 Field curvature and distortion 51

4.2.6 Modulation transfer function 52

4.2.7 Image simulation 53

Chapter 5 Conclusions 55

TABLE OF FIGURES

Figure 1.1 Photographic lens illustration 1

Figure 1.2 Flowchart diagram 3

Figure 2.1 The classification of lens 4

Figure 2.2 System descriptions and 3D layout 5

Figure 2.3 Distortions and field curvature of lens 6

Figure 2.4 The Landscape lens design by Zemax 6

Figure 2.5 Achromatic lens design by Zemax 7

Figure 2.6 Spot diagram, achromatic focal shift 8

Figure 2.7 Petzval lens design by Zemax 9

Figure 2.8 Petzval lens design by Zemax 9

Figure 2.9 Spot diagram, ray fan plot of Petzval portrait lens 10

Figure 2.10 Rapid Rectilinear lens 10

Figure 2.11 Field curvature and distortion, achromatic focal shift 11

Figure 2.12 Doublet (a), separated of doublet (b) 12

Figure 2.13 Cooke Triplet (left), H Dennis Taylor (right) 13

Figure 2.14 The Celor lens 14

Figure 2.15 Spot diagram of the Celor lens 15

Figure 2.16 The layout of Tessar lens 15

Figure 3.1 Chromatic aberration 17

Figure 3.2 Primary axial color 18

Figure 3.3 Marginal rays and thin lens 19

Figure 3.4 Two elements optical system 21

Figure 3.5 Interactive Abbe-Diagram 27

Figure 3.6 Illustration image of Cooke Triplet 28

Figure 3.7 Rear half of Cooke Triplet 29

Figure 3.8 Cooke Triplet design procedure 31

Figure 3.9 illustration of Cooke Triplet lens 33

Figure 3.10 illustration of Tessar lens 34

Figure 4.1 Rear half of Cooke Triplet design using Zemax 35

Figure 4.2 Cooke triplet 52mm, f/5 design using Zemax 37

Figure 4.3 Modulation transfer function after hammer optimization (MTF1) 38

Figure 4.4 Modulation transfer function (MTF2) 40

Figure 4.5 Modulation transfer function (MTF3) 40

Figure 4.6 Modulation transfer function (MTF4) 41

Figure 4.7 Spot diagram, modulation transfer function (MTF5) 41

Figure 4.8 System data 42

Figure 4.9 3D-layout of Cooke Triplet lens 43

Figure 4.10 Transverse ray fan plot 44

Figure 4.11 Field curvature and distortion 44

Figure 4.12 Modulation transfer function (MTF) 45

Figure 4.13 Image simulation 46

Figure 4.14 System descriptions 49

Figure 4.15 3D-layout of lens 50

Figure 4.16 Transverse ray fan plot 51

Figure 4.17 field curvature and distortion 52

Figure 4.18 Modulation transfer function 52

Figure 4.19 Image simulation 53

Figure 5.1 Double Gauss lens 56

Figure 5.2 Telephoto lens 56

Figure 5.3 Fisheye lens 56

LIST OF TABLES

Table 3-1 target of Cooke Triplet design to approach 26

Table 3-2 Glasses information 28

Table 3-3 specification of Tessar lens 32

Table 4-1 Variables use in Merit function 36

Table 4-2 Operands use in the design 39

Table 4-3 Triplet Lens data 46

Table 4-4 Aspheric data 46

Table 4-5 Cooke Triplet specifications requirement and result 47

Table 4-6 Tessar lens data 48

Table 4-7 Aspheric surface data 49

Table 4-8 Tessar lens specifications requirement and result 54

Chapter 1: INTRODUCTION

1.1 Review of photographic lens

Photographic lens (also known as camera lens) is an optical system which was the combination of several lens elements used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically (figure 1.1) Each of lens element in the system directs the path of light rays from the object to recreate the image

more interested in a fast camera lens, this mean the f-number must become large This made the task of design a new lens become more difficult because the larger f-number the lens system undergoes the more of aberration

Nowadays, with the development of technology and the computer is more powerful, design photographic lens using software become much easier and save a lot of time There are many softwares were created for optical design purposes such as Code V, Zemax, Winlens, OSLO, etc In this study, Zemax was used It is an outstanding design and simulation software that allows scientists, engineers, researchers and students to turn their optical and illumination systems ideas into reality

1.2 The aim and objectives in the study

As mentioned above, the objective here was the photographic lens (camera lens) To get a more understanding about the history of photographic lens, chapter 2 will be the review of several important classic lenses Each type of lens will be redesigned using Zemax Then the lens’s properties will be carefully analyzed to point out the pros and cons such as what kind of aberrations it was suffered from and what is the weaknesses

in the present lens Then we can understand the demands of creating new type of lens that was the solution of the previous one This is the first aim in this study

The Cooke Triplet lens and the Tessar lens were the two famous photographic lenses which were considered as the revolutions These lenses as well as their modifications are now widely used in many cameras and being the commercial products on the market

So, designing the new versions Cooke Triplet and the Tessar lens will be the second aim Every aspects of the design were showed in the chapter 4

Along with the aims of the study, some important optical theories will be mentioned also They are very useful theories that will be applied to the photographic lens design The method that was used to design two new versions Cooke Triplet and Tessar lens was exhibited in chapter 3 The whole content has been discussed through this thesis could see clearly from the flowchart diagram below

Figure 1.2 Flowchart diagram

photographic lens

review several classic lenses

redesign with zemax

analyzes propertiesoptic theories

and methods

Cooke Triplet lens

analyze

description

pre-calculation

and design

Tessar lens analyze

description

pre-calculation and designconclusions

history

Petzval

sumachromatic

power and

Celor

equation

CHAPTER 2 LITERATURE REVIEW

In present chapter, we are going to review several important classic lenses Our works will follow the order of the figure 2.1 below It is very clear and easy to understand The figure lists out the name, the number of element in each lens, which element is positive and which one is negative The time when it was invented also presented Time flow will be our direction to work out but not the number of element Each of lens will be redesigned, analyzed the advantages as well as the drawbacks The Landscape lens, Achromat Landscape lens, Petzval portrait lens, Rapid rectilinear lens and Celor lens are the main topics to be discussed in this chapter

Figure 2.1 The classification of lens

2.1 Landscape lenses

The earliest photographs were made by placing paper covered with a light-sensitive material in the focal plane of a camera obscura, the lenses used being the first simple plano-convex lenses, and later simple meniscus landscape lenses as suggested by Wollaston in 1812 (Fig 2.2) A suitably designed meniscus lens, with a stop in front of

it on the concave side of the lens, will give good pictures at f/11 or f/16, covering with moderate definition a total field of about 450 This lens is still universally adopted in low-priced cameras In addition to its cheapness, this lens has the advantage of possessing only two glass air surfaces (By Mc Graw-Hill Book Company, Inc)

Figure 2.2 System descriptions and 3D layout

The Landscape lens design by Zemax

There are two different versions of the land-scape lens: with the stop in front or with the stop behind the lens, considered from the object location Both setups are nearly equivalent in correction, but the stop in front version is more desirable, because of the resulting more familiar barrel distortion The bending effect of the lens is optimized to obtain a proper correction of astigmatism It is usual to flatten the tangential image surface, the astigmatism can-not be fully corrected, and the sagittal image surface is rather poorly corrected The bending is not optimized to correct the spherical aberration, therefore only small apertures can be used

Figure 2.2 shows a landscape lens with a stop in front of the lens in 3D layout The focal length is f = 400 mm, F-number is 15, full field of view is 2 x 250 in spectral range of

a maximum value of 2.7% The tangential image surface is better than sagittal one Figure 2.4 shows the corresponding spot diagrams for three fields A serious achromatic aberration was presented, the lack of this lens

Figure 2.3 Distortions and field curvature of lens

The Landscape lens design by Zemax

Figure 2.4 The Landscape lens design by Zemax

Spot diagram, chromatic focal shift windows

2.2 Achromatic landscape lens

The lack of achromatism of the simple meniscus landscape lens was soon found to be a disadvantage, even before the camera obscura became a photographic camera, and the achromatic landscape lens was introduced by Chevalier in 1821 (Fig 2.5) The process

of achromatization automatically removed both of the chromatic aberrations, thus improving the definition in a twofold manner

The lens was constructed as a cemented doublet, color correction and a better correction

of the spherical aberration can be performed If the negative flint lens is located towards the stop and the stop has a distance of nearly 1/5 of the focal length and is oriented to the object side, the lens is named after its invertor: a Chevalier or French landscape lens Another well-known setup due to Grubb has a similar stop arrangement, but a positive crown lens is located close to the stop Figure 2.5 shows a simple example of Grubb-type achromatic lens in 3D which has an effective focal length 400mm, f-number is 16 with the stop in front of the positive lens The ray fan plot, distortion and field curvature also are presented

Figure 2.5 Achromatic lens design by Zemax

System data, ray fan plot, 3D view, distortion and field curvature of the

achromatic lens

From the ray fan plot we can see that the spherical aberration of on axis field is better than landscape lens Let’s take a look at the spot diagram (Fig 2.6), it clearly has a smaller diameter that expresses a better performance Besides that, the chromatic focal shift presents the correction of chromatic aberration

Figure 2.6 Spot diagram, achromatic focal shift

2.3 The Petzval Portrait lens

The Landscape lens at f/11 was successfully adopted in the early daguerreotype process, but exposures of half an hour or more were necessary even in sunlight Consequently when daguerreotype portraiture was attempted the need for a much faster lens J Petzval,

of Vienna, solved the problem in 1841 by the design of his well-known portrait lens While doing portraits, people tended to fidget if exposure times exceeded a few seconds The result is some blurring of the image due to object movement This does not help customer satisfaction (Introduction to lens design: with practical Zemax example, by Geary, Joseph M) The new industry wanted and needed a faster lens, hence they held

a contest Petzval’s design was an f/3.6 (figure 2.7), about twenty times faster than the lenses then on the market

The setup for a Petzval portrait lens consists of two part with the stop lying between them In the optimization process, we have to satisfy two important design constraints The first is that the stop will be held midway between the two lens groups This is done

by slaving the rear-stop airspace to the front-stop airspace The second constraint is that the ratio of the system focal length to the back focal length be equal to two In the example, we are going to design a 125mm EFL, f/5, cover a field of 200 In comparison with the landscape lens, it is clearly that the Petzval lens shows rather better performance With the F-number of 5 it is a much faster lens From the figure 2.7 we can see the 3d view as well as the miscellaneous system data of the lens

Figure 2.7 Petzval lens design by Zemax

System data, 3D-layout of lens

Besides that, the chromatic focal shift plot (figure 2.8) presented the correction of chromatic aberration, both of color aberrations has been corrected significantly The field curvature is just approximately 0.05 inch and distortion of 0.9%

Figure 2.8 Petzval lens design by Zemax

Field curvature and distortion, chromatic focal shift graph

From the ray fan plot we can see that the spherical aberration of on axis field is better than that of landscape lens Let’s take a look at the spot diagram (Fig 2.9), diameters are smaller compare to that of landscape lens that express a better performance Notably, the Petzval portrait lens is not a symmetrical It suffered from the disadvantage of astigmatic defects in the outer part of the field, which could not be removed so long as the designer was limited to the use of ordinary crown and flint glasses

Figure 2.9 Spot diagram, ray fan plot of Petzval portrait lens 2.3.1 Rapid Rectilinear lens

In 1866, Dllmeyer and Steinheil simultaneously and independently realized that if two identical lenses are mounted symmetrically about the central stop, the three transverse aberration-distortion, chromatic difference of magnification, and coma, are automatically removed and hence each component of such a symmetrical system need not be corrected for any of these aberrations They therefore constructed a symmetrical lens, each half of which was corrected for longitudinal chromatic and spherical aberration; the astigmatism was then removed by placing the stop at the correct position relative to each component In this way they produced the well-known Rapid Rectilinear

or Aplanat lens (Fig 2.10)

Figure 2.10 Rapid Rectilinear lens

System description, 3D-layout of the symmetrical lens

It is a symmetric achromat which made use of two glasses whose Abbe numbers were not that far apart This allows for a more compact wide field lens design, and a flatter illumination field In our design example, LF1 and F1 glasses were used The lens has

an effective focal length of 254mm, f/8 and cover a field of 400 Also, the figure 2.11 points out that the problem of distortion was improved, just 0.05% The color correction was guaranteed

From this point of design process, if we continue optimize the lens system by breaking the symmetry of the lens, it can be better This is a reasonable thing to do when the object-image conjugates are themselves unsymmetrical

Figure 2.11 Field curvature and distortion, achromatic focal shift

2.4 The Cooke lens

Since it was born in early of 19th century, the camera development progress has undergone several revolutions to obtained achievement today Among these was the famous invention by H Dennis Taylor in 1893 of the Cooke Triplet lens

As optical manager of T Cooke & Sons of York, makers of astronomical telescopes,

H Dennis Taylor attempted to eliminate the optical distortion or aberration at the outer edge of lenses In 1893 he designed and patented the revolutionary, and now famous, Triplet design (British patent no 1991) His work was done in algebra and calculus, without trigonometry Taylor’s methods were to do preliminary calculations, fabricate and a prototype lens, test it to find its good and bad points, then go back to his calculations and tweak his design

The major problem with the lenses of the time remained astigmatism and field curvature near the edges of the image Taylor realized that if he took a thin positive and thin negative lens of the same power and placed them in contact (Figure 2.5a), they would have a zero Petzval sum (meaning they would have a perfectly flat field) It would also have zero power, meaning it didn’t magnify or focus the image If he separated the two elements (Figure 2.5b), however, the lens would begin to have significant positive power, but would retain a zero Petzval sum, meaning the field of focus would still not

be curved

Figure 2.12 Doublet (a), separated of doublet (b)

There was a problem, however Most lenses of the day were symmetrical about a central stop (aperture), because such symmetry eliminated a lot of aberrations The unsymmetrical lens would have horrible lateral aberrations Taylor determined that if

he split one of the elements in two, mounting each of the split elements on either side

of the remaining element, the lens would be more symmetric and the aberrations decreased He patented both possible combinations in 1893, but preferred the negative element in the center, surrounded by the two halves of the positive element

The Triplet lens consists of a negative lens placed between two positive lenses The negative lens using flint glass which has low Abbe number or high dispersion Vice versa, the positive uses the crow glass with low dispersion Using smallest number of elements, having 14 degree of freedom (six curvatures, three lens thickness, three glass types, two airspaces), it was the first photographic lens that allowed the reduction of the third order aberrations (spherical, coma, astigmatism, field curvature and distortion) and the first order one (axial color chromatic, lateral chromatic) to a value close to zero

Figure 2.13 Cooke Triplet (left), H Dennis Taylor (right)

This was a successful design, the original aperture was f/4.5, but this was increased to f/2.8 Then by splitting and/or compounding the three elements a wide variety of triplet derivatives were produced The Zeiss Tessar lens, designed independently in 1902 by Rudolph and in production ever since, is one of the best known of these

Being different, the Triplet allowed a different set of modifications Over 80 patents have been issued for variations and modifications of the Cooke Triplet, more than for any other type of lens Nowadays, with the aid of computer software, achievements of science and technology, especially the advancement in coating technique, it allows us

to design and develop a more and more excellent lens with higher quality base on Cooke

Triplet design

2.5 The Celor lens

In connection with the Cooke lens above, it was mentioned that the Petzval sum can be reduced by separating the positive and negative element of an achromatic doublet If two such separated doublets are mounted symmetrically about a central stop, a lens is obtained which offers even more possibilities for a good design that does the Cooke lens Two independent series of designs based on this general principle have been developed, one in which the four lenses are all biconvex or biconcave and the other in which all four lenses are meniscus-shaped The first form is exemplified by the Goerz Celor f/4.5, designed by von Hoegh in 1898 (Fig 2.22) Later modifications of this type are the Goerz Dogmar, the Steinheil Unofocal, and the Taylor-Hobson Aviar (Mc Graw-

Figure 2.14 The Celor lens

System descriptions, field curvature and distortion, chromatic focal shift

and the 3D layout

Here, we will do an example design of Celor lens using Zemax The lens has 125 mm effective focal length with f-number of 6, using BAF4 and SK4 glasses for F, d, C spectrum, cover a field of view of 400 It is a symmetric lens with a pair of air-spaced achromats The air-space provides a new degree of freedom, means that the individual lens powers must increase to preserve the color correction This can also be done in such a way as to lower the Petzval sum Besides that, try to control spherical aberration and astigmatism in the design process The symmetry of the lens system helps to reduce the coma, distortion and lateral color Figure 2.23 show the spot diagram which has a small dimension compare to previous type of lens

Figure 2.15 Spot diagram of the Celor lens

2.6 The Tessar lens

By cementing together the rear elements of an unsymmetrical Celor-type lens, Rudolph

in 1902 produced the Tessar lens (Fig 2.24) which is probably the best known and most generally used type of lens produced in recent times Tessar comprises four elements in three groups, one positive crown glass element at the front, one negative flint glass element at the center and a negative plano-concave flint glass element cemented with a positive convex crown glass element at the rear The airspaces are adjusted to fulfill the Petzval sum

Figure 2.16 The layout of Tessar lens

As common belief, the Tessar was considered as a variant of the 1893 Cooke triplet design by replacing the rear element with a cemented achromatic doublet In fact, Paul Rudolph designed the Anastigmat with two cemented doublets in 1890 In 1899, he separated the doublets in the Anastigmat to produce the four-element, four-group Unar lens In 1902, he realized that reversing the two rear elements of the Unar and returning

to a cemented doublet would improve performance; he named the result "Tessar" The Tessar lens has been made in apertures ranging from f/15 as an apochromatic process lens, down to f/2.7 for cine purposes The field runs from 45 to 750, depending on the aperture and focal length

CHAPTER 3 USEFUL OPTIC THEORIES AND METHODS

3.1 Useful optic theories

3.1.1 The derivation of primary axial color equation

In real optical system design we are not only facing with monochromatic aberrations but also the complexity design problems with chromatic In optics, chromatic aberration

is an effect resulting from dispersion in which there is a failure of lens to focus all colors

to the same convergence point It occurs because lenses have different refractive indices for different wavelengths of light

There are two types of chromatic aberration: axial (longitudinal, figure 3.1a), and transverse (lateral, figure 3.1b) In this part, we will derive an equation for axial color which give the actual separation between the red and blue foci

(a)

(b)

Figure 3.1 Chromatic aberration

(a) Axial chromatic aberration, (b) Transverse chromatic aberration

Figure 3.2 Primary axial color

In Zemax, we usually use three wavelengths named F, d, C which respectively represent for blue, green and red color

We know that the power of a thin lens is given by:

 n 1  C1 C2 (3.1)

   Where n is the refractive index of glass C is the denotation of curvature of lens

Take derivative of equation 2.1, the change in power as a function of index:

From equation 3.5 we found that the power difference is equal to power in d-light divided by the Abbe number Rewrite this as:

1 (3.6)

d v



 

In other word, power can be described in term of focus

1 (3.7)

f

 Taking the derivative:

Figure 3.3 Marginal rays and thin lens

We will now find the form for df that incorporates the marginal ray height and angle Multiply both sides by square of y:

2 2

2 d (3.10)

d

y y

In almost optical design, we consider the object is at infinity, and with a given effective focal length, u’ will not affect to df Then, to correct to axial color aberration we should consider the other part of equation 3.11 to be equal zero

For multiple element optical system we have:

3.1.2 Field curvature flattening

When forming an image of a plane object through an optical system but what you get

is a curve image plane and one of the culprits is the field curvature aberration In fact,

in an optical system, as the chief ray angle is varied, the image point traces out a curved focal surface as a function of chief ray angle This curve image surface is also called Petzval curvature

In Seidel aberration equations, Petzval field curvature is given by:

Let’s consider a two-surface system Then:

The factor in brackets is the power of a thin lens Hence the sum becomes:

2

220 (3.17)

4

j P

j

L W

From equation 3.17 we found that the Petzval field curvature aberration depends solely

on the powers and refractive indices of the components elements Consequently, if the sum is small enough we will have a reasonable flat field

3.1.3 Power equation for multiple elements optical system

Optical power is the degree to which a lens, mirror, or other optical system converges

or diverges light It is equal to the reciprocal of the effective focal length(  1/ f)and have unit of inverse metre For a system consisting two elements separate by a distant

x, the optical power equation is given as:

Figure 3.4 Two elements optical system

In geometrical optical, we used to work with pair of linear paraxial ray tracing

h h

    

3.1.4 Celor equation derivation and apply for Cooke triplet design

Emil von Hoegh was born in 1865 He was a chief optical designer for the German company Goerz, a major manufacturer of photographic objectives He designed many lenses during his time at Goerz

Among these was the famous Celor lens and his Celor equation is a good method to find out the starting point of many others design And here, we will look back to the derivation of this equation again

The following constraints are imposed on the design of Celor rear half:

 Is represented for Petzval sum

The equation No.1 is the generalized power condition No.2 is the constraint on axial color and No.3 is the constraint on the Petzval sum

From the constraint No.1 we have:

 

2 2