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Aberration document explaining the Seidel coefficients
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  S-118.4250   P OSTGRADUATE SEMINAR ON ILLUMINATION ENGINEERING ,   S PRING 2008 L IGHTING U NIT ,   D EPARTMENT OF E LECTRONICS ,   H ELSINKI U NIVERSITY OF T ECHNOLOGY (TKK) O PTICAL P ERFORMANCE : CHARACTERIZATION OF A PUPILLOMETRIC CAMERA   Petteri Teikari , petteri.teikari@gmail.com   Emmi Rautkylä , emmi.rautkylä@tkk.fi   ABSTRACT  The object of this work is to help to understand the process of characterizing a camera used in pupillometric research. In our case, the characterization consists of measuring geometric aberrations, sharpness (MTF) and noise and determining the dynamic range. Finally some ways to compensate the noticed flaws are presented.  TABLE OF CONTENTS  A  BSTRACT ..................................................................................................................................1   T  ABLE OF CONTENTS ................................................................................................................2   1   I NTRODUCTION .................................................................................................................3   2   O PTICS &   I MAGING ...........................................................................................................4   2.1   Structure of lenses and their optical characteristics................................................................4   2.1.1   Focal length...........................................................................................................................5   2.1.2    Aperture.................................................................................................................................6   2.1.3   Image formation...................................................................................................................7   2.1.4   Depth of field (DOF)...........................................................................................................8   2.1.5   Modular transfer function (MTF) and contrast................................................................10   2.2   Noise.........................................................................................................................................12   2.3   Dynamic range.........................................................................................................................14   2.4   Optical aberrations..................................................................................................................15   2.4.1   Chromatic aberration..........................................................................................................15   2.4.2   Geometric aberrations........................................................................................................16   2.4.3    Vignetting............................................................................................................................18   2.4.4   Diffraction...........................................................................................................................19   2.5    Aberration correction..............................................................................................................20   3    A  PPLIED LENS DESIGN ....................................................................................................22   3.1   Measurement science & Machine vision................................................................................22   3.2   Photography.............................................................................................................................24   4   C HARACTERIZING OPTICAL PERFORMANCE IN PRACTICE ..............................................25   4.1   Pupillometry & overview of the setup...................................................................................25   4.2   Methods....................................................................................................................................25   4.3   Results of the measurements..................................................................................................27   4.3.1   Modulation transfer function and sharpness....................................................................27   4.3.2   Geometric aberrations........................................................................................................29   4.3.3   Dynamic range....................................................................................................................30   4.3.4   Noise....................................................................................................................................31   4.4   Image restoration.....................................................................................................................31   4.4.1   Sharpness.............................................................................................................................31   4.4.2   Geometric aberrations........................................................................................................31   4.4.3   Dynamic range....................................................................................................................31   4.4.4   Noise....................................................................................................................................32   4.5   Conclusions..............................................................................................................................33   5   D ISCUSSION .....................................................................................................................35    A  PPENDICES ............................................................................................................................36    Appendix 1: The Matlab code for an ideal image...............................................................................36    Appendix 2: The Matlab code for an image with coma......................................................................37    Appendix 3: The Matlab code for averaging monochrome images...................................................38    Appendix 4: The Matlab code for image quality calculation..............................................................39    Appendix 5: The Matlab code for calculating variance of one row in the image.............................40   6   R  EFERENCES ...................................................................................................................41    O PTICAL PERFORMANCE :   C HARACTERIZATION OF A PUPILLOMETRIC CAMERA  T EIKARI &   R   AUTKYLÄ  I NTRODUCTION  3 S  TRUCTURE OF LENSES AND THEIR OPTICAL CHARACTERISTICS   1 INTRODUCTION Cameras do not 'see' in the same way those human beings are able to. They are not equivalent to human optics because their lens design defines how the image is formed. Therefore, if cameras are to be used in research purposes, it is important to know how to minimize the effect of the lens system on the research data.  The object of this work is to help to understand the process of characterizing a camera. Under special examination is a pupillometric camera, hence a camera used for providing data about the autonomous nervous system by recording pupil size and dynamics. The experimental part of the paper gives a practical example of characterizing such pupillometric camera very sensitive to aberrations and noise and discusses possible ways to improve the image quality. That, together with the discussion, forms the core of the paper and raises questions for experiments to come.  The work is meant for people not very familiar with optics or pupillometry. It takes a simple approach to the optics and imaging in Chapter 2. Chapter 3, for one, gives more insight to metrology  with a review of more specific lens design used in machine vision and measurement science applications.  O PTICAL PERFORMANCE :   C HARACTERIZATION OF A PUPILLOMETRIC CAMERA  T EIKARI &   R   AUTKYLÄ  O PTICS &   I MAGING  4 S  TRUCTURE OF LENSES AND THEIR OPTICAL CHARACTERISTICS   2 OPTICS & IMAGING In this chapter basic concepts of optic systems are reviewed in the detail needed for this work. 2.1 S TRUCTURE OF LENSES AND THEIR OPTICAL CHARACTERISTICS   Lens or lens system is the optical structure that defines how the image is formed. In practice there are always several lenses (basic types illustrated in Figure 1 [1]  ) in ‘the lens’ that can be bought from a store and therefore in this work the word lens refers to the lens system. Lenses can be categorized roughly to wide-angle and telephoto lenses where wide-angles have larger angle of  view (with smaller focal length) and telephoto lenses have smaller angle of view (with larger focal length). Lenses can either have a fixed focal length (prime lenses) or it can be changed for example from wide-angle to telephoto when they are commonly referred as zoom lenses. Lenses could be characterized also according to their lens design and the number of elements but that kind of characterization is beyond the scope of this work. Figure 2 demonstrates the typical structure of a lens for commercial digital cameras. The lens is mounted on the camera using specific bayonet mounts [2]  which are poorly intercompatible in commercial cameras even though there exist adapters to fit different bayonets to a given camera. In machine vision cameras typically there are three bayonet types [3] : 1) CS-mount, 2) C-mount, and 3) M12x0.5 (metric threads). C-mount is most commonly found from mid-range to high-end optics whereas CS-mount is a bit rarer but a CS-mount lens can be fitted into a C-mount using a proper spacer. The flange (back focal) distance is different for C- and CS-mounts, for C-mount it is to the sensor 17.52mm whereas it is 12.52mm for CS-mount [4] . C-mounts are often found from microscopes too. M12x0.5 is found from cheaper cameras. Zoom wheel is used to change the focal length if the focal length is not fixed which is however the case with many machine vision lenses.  Aperture controls the amount of light reaching the image forming surface (film or sensor).  Aperture is practically always found from all lenses and in commercial lenses it can be adjusted but again in many machine vision lenses the aperture is fixed. In machine vision lenses it is not common to have an image stabilizer which  would allow longer exposures with comparable image sharpness to shorter exposure without the image stabilizer. In low light level situations image stabilizer can significantly enhance the image quality. Focus wheel or similar structure then is used to make image sharp. In following chapters the basic optical characteristics of lenses are reviewed. Figure 2. Illustration of the typical structure of an objective used in SLR-cameras. It should be noted that in most of the machine vision lenses there is no possibility to adjust the focus, the focal length (zoom adjustment) or the aperture as they are all fixed. Also image stabilizer is hardly ever found from objectives intended for machine vision applications. (Picture: Tuomas Sauliala).   Figure 1. Lenses classified by the curvature of the two optical surfaces [1] .  
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