The revolution and design of photographic lens with zemax

逢 甲 大 學 電機工程學系碩士班 碩士論文 Zemax 軟體模擬攝影鏡頭的設計 The Revolution and Design of Photographic Lens with Zemax 指導教授：李企桓 研 究 生：Dang Xuan Du 中 華 民 國 一 百 零 五 年 六 月 The Revolution and Design of Photographic Lens with Zemax i FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 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 ii FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 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 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 iii FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax CONTENTS Chapter 1: INTRODUCTION 1.1 Review of photographic lens 1.2 The aim and objectives in the study CHAPTER LITERATURE REVIEW 2.1 Landscape lenses 2.2 Achromatic landscape lens 2.3 The Petzval Portrait lens 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 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 RESULTS 35 4.1 The Cooke Triplet lens 35 4.1.1 The progression 35 iv FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 4.1.2 4.2 Final results and comparison 42 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 Conclusions 55 v FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax TABLE OF FIGURES Figure 1.1 Photographic lens illustration Figure 1.2 Flowchart diagram Figure 2.1 The classification of lens Figure 2.2 System descriptions and 3D layout Figure 2.3 Distortions and field curvature of lens Figure 2.4 The Landscape lens design by Zemax Figure 2.5 Achromatic lens design by Zemax Figure 2.6 Spot diagram, achromatic focal shift Figure 2.7 Petzval lens design by Zemax Figure 2.8 Petzval lens design by Zemax 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 vi FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 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 vii FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 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 viii FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax optimized meticulously and more precisely In experience, this will help Zemax give out a better results when we use the aspheric surfaces Figure 4.9 3D-layout of Cooke Triplet lens Up (Zemax 6- optical design), down (Owner design) The next analysis window is ray fan plot that showing in the figure 4.10 From these windows we can estimate how well the aberrations have been controlled in each design At the same maximum scale of 100 micrometer, the ray fan of our design is much better, it is much flatter in both tangential and sagittal planes The flat of the on axis field ray fan tell us the Seidel spherical aberration presented is very small The Coma and Astigmatism are also pretty small Inversely, the aberrations in the design that we take as example for comparison is bad, this can be easily recognized when looking at the picture on the left of the figure 43 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Figure 4.10 Transverse ray fan plot Left (Zemax – Optical Design), right (Owner design) The other aspect of a photographic lens design we should take care about is the field curvature and distortion A flat field curvature plot allowed a flat image sensor, so it is important for a photographic lens to get a reasonable flat field curvature Let’s make a comparison between the two designs It is clearly that in our design, the field curvature is much better and much flatter at the same scale of 0.5, its maximum value is just 0.06 mm The distortions is a little large, it is about 1.45% while the other is 0.5% but that is still good and lower than the 2% of requirement Figure 4.11 Field curvature and distortion Left (Zemax – Optical design), right (Owner design) 44 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Modulation Transfer Function (MTF) is an important method of describing the performance of an optical system MTF describes the contrast in the image of a spatial frequency presented in the scene being viewed In other word, MTF describes the transfer of modulation from the object to the image as a function of spatial frequency and is commonly used to specify lens performance, and as optimization and tolerance targets during lens design If we take notice at the table in the chapter that list out the requirement for the Cooke Triplet design, we can see that the MTF is the major criteria Figure 4.12 shows the MTF of the two design On the right is one for our design which has a good performance At the limited resolution of 50lp/mm, all the fields have their MTF value up to 0.5 and almost 0.8 for the on-axis field Figure 4.12 Modulation transfer function (MTF) Left (Zemax – Optical design), right (Owner design) Finally, for a more intuitive we will compare the two pictures that take from the two Cooke Triplet lens via image simulation analysis window of Zemax From the figure 4.12, the picture on the left is darker, cause of using too much vignetting factor in design The outside of the picture is darker and blur that shows a low quality of the lens for larger fields Contrarily, the picture on the right which is the result from our Cooke Triplet lens is brighter, sharper It is because of better MTF, well controlled in aberrations as well as the correction of chromatic aberration Our design also used just a small amount of vignetting, so more light rays can pass through the system, it means a brighter in the final image Table 4.3 and 4.4 show the last lens data and aspheric data of the Cook Triplet lens 45 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Figure 4.13 Image simulation Left (Zemax – Optical Design), right (Owner design) Table 4-3 Triplet Lens data # Type STANDARD EVENASPH EVENASPH EVENASPH EVENASPH STANDARD EVENASPH STANDARD STANDARD STANDARD Comment Curvature 0.00E+00 5.94E-02 -1.06E-02 -5.37E-03 8.89E-02 0.00E+00 -3.27E-02 -5.35E-02 0.00E+00 0.00E+00 Thickness 1.00E+10 5.00E+00 4.93E-01 9.99E-01 3.00E+00 3.00E+00 1.55E+00 4.09E+01 -1.91E-02 0.00E+00 Glass Semi-Diameter 0.00E+00 N-LASF31 8.97E+00 7.94E+00 SF13 7.09E+00 5.79E+00 5.16E+00 N-LASF31 6.35E+00 6.50E+00 1.92E+01 1.92E+01 Table 4-4 Aspheric data Conic 0.00E+00 -1.02E+00 5.66E+00 6.02E+00 -8.05E-02 0.00E+00 -5.37E+00 0.00E+00 0.00E+00 0.00E+00 Parameter 0.00E+00 5.35E-06 6.05E-05 7.79E-05 1.05E-05 0.00E+00 5.77E-07 0.00E+00 0.00E+00 0.00E+00 46 Parameter 0.00E+00 -8.61E-08 -6.70E-07 -1.35E-06 -7.08E-07 0.00E+00 2.41E-07 0.00E+00 0.00E+00 0.00E+00 Parameter 0.00E+00 -2.53E-10 3.03E-09 6.81E-09 -2.80E-09 0.00E+00 1.53E-09 0.00E+00 0.00E+00 0.00E+00 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Table 4-5 shows all the specifications of the final Cooke Triplet lens While the left picture shows the standard requirements for the design, the right one shows the results It is easy to recognize that all of the required specifications were well response They are include effective focal length that equal to 52mm, the full field of view of 40 degree, total length of the lens system, distortion, relative illumination, chromatic aberrations, ray fan plot, and especially, the modulation transfer function (MTF), its performance was beyond the standard at both limited resolutions and ½ Nyquist frequency Besides that, at some filed the modulation transfer function for the tangential (MTFT) field is better than sagittal (MTFS) field that is the sign of a good design Table 4-5 Cooke Triplet specifications requirement and result TRIPLET LENS Specification sensor type EFFL FOV F-number Total track Max image circle Optical distortion Relative illumination lateral color Axial color Ray fan focus MTF on axis 0.57 0.82 TRIPLET LENS require Specification 35mm full frame 24x26; pixel pitch 10µm 52mm 40 50% < x pixel pitch (10µm) corrected (8fields) < x pixel pitch (20µm) infinity 25 lp/mm 50 lp/mm S T S T 85% 85% 60% 60% 70% 70% 50% 50% 70% 70% 50% 50% 60% 60% 40% 40% 47 sensor type EFFL FOV F-number Total track Max image circle Optical distortion Relative illumination lateral color Axial color Ray fan focus MTF on axis 0.57 0.82 result 35mm full frame 24x26; pixel pitch 10µm 52mm 40 54.9 mm 39 mm 1.40% 75% 4.17 µm corrected (8fields) < x pixel pitch (20µm) infinity 25 lp/mm 50 lp/mm S T S T 90% 90% 79% 79% 86% 87% 71% 74% 87% 86% 70% 60% 69% 71% 51% 52% FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 4.2 Tessar lens f/2.8, 52mm In this study, a Tessar lens f/2.8, 52mm was designed for the photographic purpose The lens include lens components with four lenses element The two outside elements were the positive and made by the crown glass with high index and low dispersion Both negative elements were made by flint glass with lower index and higher dispersion The reason is for the correction of achromatic aberration as well as Petzval sum and highorder aberrations The lens was design for the CCD sensor which has pixel pitch of 10 µm, it mean that the limited resolution in this case is 50 lp/mm 4.2.1 Lens data This Tessar lens was designed based on the structure of an f/3.5, 52mm Cooke Triplet lens by splitting the rear element to two elements without separation So the first step is design a raw Cooke Triplet which have a basic quality of performance Then split it rear element to get a raw Tessar lens Next, use Damp Least Square algorithm to optimize the system to get a better performance Last, used a numbers of variables, aspheric surface, vignetting, combine with Hammer optimizer, undergone many long processes of optimization and adjustment we could get the final design of Tessar lens All the lens data and aspheric data showed in the table 4-5 and 4-6 below Table 4-6 Tessar lens data # 10 Type STANDARD STANDARD EVENASPH EVENASPH EVENASPH STANDARD EVENASPH STANDARD EVENASPH STANDARD STANDARD Comment Curvature 0.00E+00 5.10E-02 1.45E-02 2.52E-02 7.87E-02 0.00E+00 -1.89E-02 7.01E-02 -2.45E-02 0.00E+00 0.00E+00 48 Thickness 1.00E+10 6.64E+00 1.99E+00 1.44E+00 7.84E+00 2.47E+00 1.10E+00 7.45E+00 3.63E+01 1.60E-03 0.00E+00 Glass TAFD6 S-TIH11 FN11 S-LAH55 Semi-Diameter 0.00E+00 1.45E+01 1.36E+01 1.10E+01 8.50E+00 6.69E+00 7.90E+00 9.30E+00 9.70E+00 1.88E+01 1.88E+01 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Table 4-7 Aspheric surface data Conic 0.00E+00 0.00E+00 6.01E+00 8.24E-01 4.98E-01 0.00E+00 -5.00E+01 0.00E+00 -5.86E+00 0.00E+00 0.00E+00 Parameter 0.00E+00 0.00E+00 1.14E-05 2.54E-05 7.67E-06 0.00E+00 3.50E-06 0.00E+00 1.87E-05 0.00E+00 0.00E+00 Parameter 0.00E+00 0.00E+00 -7.86E-08 -3.70E-07 -2.61E-07 0.00E+00 6.95E-07 0.00E+00 1.48E-07 0.00E+00 0.00E+00 Parameter 0.00E+00 0.00E+00 1.45E-10 1.06E-09 -1.17E-09 0.00E+00 9.35E-11 0.00E+00 1.09E-09 0.00E+00 0.00E+00 4.2.2 System descriptions To estimate the quality of this Tessar lens, a comparison of it with another version will be made here That is another Tessar lens which was patented by US Both of them have relative similar description as listed in the figure 4.14 They are photographic lens which have effective focal length of 52mm and cover 400 field of view with the object is at infinity For more effectively optimize, the half field of view in our system was divided in 11 fields Figure 4.14 System descriptions Left (Owner design), right (http://www.freepatentsonline.com/3895857.pdf) 49 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 4.2.3 Layout of lens Let’s take a look at the 3d-layout of the two design They are both different In our design the aperture stop has been located at the middle that make the system was more symmetry So it easier to reduce the Coma, lateral color aberrations, especially harmonize the Petzval sum In opposite, the patented version which has a behind aperture stop and it was hard to control the aberrations The glasses must be higher index to reduce Petzval sum The lens thicknesses and airspaces have reduced to avoid cutting of marginal ray by the stop Behind-stop is good for compact film camera but not properly for instrument using CCD (CMOS) sensor Figure 4.15 3D-layout of lens Top (Owner design), bottom (http://www.freepatentsonline.com/3895857.pdf) 50 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 4.2.4 Ray fan plots The ray fan plot is the plot that tell us the different distance of the ray pierces on the image plane relative to the chief ray pierce The primary purpose of the ray fan plot is to determine what aberrations are present in the system For a good optical system, the ray fan must be as flat as possible Look at the figure 4.16 on the left, it is the ray fan plot of our Tessar It look much flatter than the one on the right, that mean the aberrations was well controlled Figure 4.16 Transverse ray fan plot Left (Owner design), right (http://www.freepatentsonline.com/3895857.pdf) 4.2.5 Field curvature and distortion As discussed in layout section, for the behind stop it is difficult to control the Petzval sum That is the reason why the field curvature as shows figure 4.17 of the patented version was not as well as our design In the same maximum scale of 0.5, in our design, all the tangential and sagittal field curvature plots close to the Y axis, they are almost flat Now, let’s take distortion into account In the patented version, the distortion is somewhat better While its value was just 0.4%, the distortion in our design was 0.75% But it was not a matter, as usual for photographic lens the distortion less than 2% can be accepted 51 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Figure 4.17 field curvature and distortion Left (Owner design), right (http://www.freepatentsonline.com/3895857.pdf) 4.2.6 Modulation transfer function Picture on the left of figure 4.18 show the MTF of the final Tessar lens All the tangential and sagittal plot of all 11 fields are close to each other and close together At the limited resolution of 50 lp/mm all MTF values are more than 60% and more than 80% at the ½ Nyquit frequency This is a good MTF of photographic lens which has been design for using with the 10µm pixel pitch of CCD sensor When compare to the MTF of the patented one, it is obviously much better Figure 4.18 Modulation transfer function Left (Owner design), right (http://www.freepatentsonline.com/3895857.pdf) 52 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax 4.2.7 Image simulation Finally but more understandably to assess the performance of the lens, that is image simulation The picture on the right of figure 4.19 is blur both at the center and the edge Especially, at the rim of the picture it is darker and not as clear as the picture on the left Inversely, the left picture look brighter and sharper than the right one In conclusion, our Tessar lens has a better quality of performance compare to the patented one Figure 4.19 Image simulation Left (Owner design), right (http://www.freepatentsonline.com/3895857.pdf) For an overall observation every aspects of the Tessar lens design, table 4-8 also shows the final results All the value on the right table demonstrated that the lens was well met the requirements The Tessar lens which has f-number of 2.8, 52 mm effective focal length and cover 40 degree field of view The distortion is very low, just 0.8% The relative illumination that defined the intensity of illumination per unit area of image surface normalized to the illumination at the point to the point in the field which has maximum illumination Its value was 75%, far better than 50% of the standard one The chromatic aberration include axial color aberration and lateral color was pretty good The design has a good ray fan plot which has maximum of 25 µm A good ray fan means third order and higher order aberration were well balanced The most important criteria of this design is the modulation transfer function From the table, MTF value of all fields were met or even higher than the requirements Additionally, the MTFT was better than MTFS at some fields In summary, a good Tessar lens was derived 53 FCU e-Theses & Dissertations (2016) The Revolution and Design of Photographic Lens with Zemax Table 4-8 Tessar lens specifications requirement and result TESSAR LENS Specifications sensor type EFFL FOV F-number Total track Max image circle Optical distortion Relative illumination lateral color Axial color Ray fan focus range MTF on axis 0.57 0.82 TESSAR LENS require Specifications 35mm full frame 24x26; pixel pitch 10µm 52mm 40 2.8 50% < x pixel pitch (10µm) corrected resonable infinity 35 lp/mm 70 lp/mm S T S T 85% 85% 70% 60% 80% 80% 60% 60% 70% 70% 50% 50% 70% 70% 50% 50% 54 sensor type EFFL FOV F-number Total track Max image circle Optical distortion Relative illumination lateral color Axial color Ray fan focus range MTF on axis 0.57 0.82 result 35mm full frame 24x26; pixel pitch 10µm 52mm 40 2.8