Optical System Image Irradiance Simulations

Transcription

1 Optical System Image Irradiance Simulations Marie Côté John Tesar Breault Research Organization, Inc. (BRO) Tucson, AZ USA June 1998 Copyright 1998, Society of Photo-Optical Instrumentation Engineers (SPIE). This paper will be published in the proceedings from the June 1998 International Optical Design Conference held in Kona, Hawaii, and is made available as an electronic reprint (preprint) with permission of SPIE. Single print or electronic copies for personal use only are allowed. Systematic or multiple reproduction, or distribution to multiple locations through an electronic listserver or other electronic means, or duplication of any material in this paper for a fee or for commercial purposes is prohibited. By choosing to view or print this document, you agree to all the provisions of the copyright law protecting it. The goal of this paper is to construct an irradiance simulation at an image. We will demonstrate a software routine written by Alan W. Greynolds (Vice President of Technology, BRO) for passing bitmap images through a lens system, and directly viewing the changes to the image caused by 1) the lens itself, 2) sources outside of the field of view, or 3) defects in manufacture. The routine calls the EMITTING DATA command, which is a new feature in ASAP 6.0 from BRO. The routine is another way to evaluate a lens system and see the effects of irradiance modeling and more. The dynamic range covered by this simulation is not limited to 1-bit, 8-bit, or 24-bit images. The distribution file is based on the full floating point precision of the computer and is accurate to seven significant digits. This method will accommodate any dynamic range the user wants. Traditionally, one would place a uniform Lambertian source at the object, trace the rays through the system, and evaluate the irradiance distribution at the detector, which is the integration of all rays that can be captured by the system, as seen in Figure 1. Figure 1. Integration of all the rays that can be captured by the system From this figure, you can see a drop-off at the corners, the result of vignetting and cosine effects in the lens system. In the example that we have chosen to model, the angular irradiance fall-off is proportional to a single cosine because the design is very nearly telecentric. While a great deal of information can be learned from plots like Figure 1, only designers with considerable experience can fully evaluate ray fans, Point Spread Functions (PSF), Modular Transfer Function (MTF) the usual

2 cast of characters and accurately predict how a system will behave under varying conditions. The value of the method presented here is straightforward. No interpretation of graphs is required. It is a software simulation of the real process. Rays emanate from a source, pass through a system, and are collected and evaluated at the detector. A graphical representation of the process is shown in Figure 2. A red bitmap image is shown on the left, which will be passed through the lens and be seen up-side-down on the right side of the figure. A five-leaf iris was placed in the lens system to demonstrate the robustness of the method, and can be seen in a ghost analysis of the system. Additionally, other defects such as scratches and defocus are modeled in subsequent figures. Lens assembly with 5 leaf iris CCD Red bitmap Figure 2. Graphical representation of red bitmap and lens assembly with five-leaf iris The camera lens that we used for all simulations comes from U.S. Patent 5,706,141, issued in January 1988 and published in Optics and Photonics News in March 1998 (page 45). It is a digital still camera lens with a short focal length of 5.26 mm, F/2.8, and the total field of view is 49.2 degrees. The diagonal of the 640-by-480 CCD used with this lens is 4.7 mm, so each pixel is approximately 6 µm. The Nyquist frequency is then about 85 lines per mm. Some amount of vignetting at full field could be seen in a layout. From the ray fan plot, the vingnetting appears close to 80%. There is some distortion, but it is a well corrected lens. This software simulation could be highly useful in modeling systems with high distortion such as endoscopes or wide angle lenses that are not as well behaved as in this example. The images for this paper were obtained in following manner. A 24-bit (.bmp) image containing r, g, b (red, green, blue) wavelengths was selected. The routine then created three separate distribution files, corresponding to the irradiance pattern found in each color. The three ray sets were traced through the system and stored, five million rays for each wavelength. They were recombined to form a single bitmap that reflects the sum of all aberrations in the lens, and the bitmap was scaled to handle the maximum flux of any one of the three files. The simulation can

3 consider system anomalies found at a particular wavelength; for example, the blue. The file containing the blue wavelength will be weighted to reflect this effect in the final recombined bitmap image. The ray generation is a Monte-Carlo method, and the rays have the same flux, but their density is proportional to the irradiance pattern of the source distribution 1. The function to convert an irradiance distribution to a source is based on the raster and includes the total number of pixels. The rise of the vector corresponds to the change in value of one individual pixel to the next. If the change between two pixels is zero then the step is zero for that point in the function. The source is created with all rays that have the same flux, and the image or distribution file is the result of a weighted random number generator operating between zero and one. If the step height is almost zero, the possibility is remote that the random number generated will create a ray within the corresponding pixel. However, within a pixel associated with a high step, more rays are created. The economy of this method is that rays are only created where they are needed, where there is a high irradiance value in the source. In turn, this saves time and speeds the process. The method improves the subjective image quality of the bitmap, unlike generating a uniform number of rays per pixels, where they often add little in terms of information. The beauty of a Monte-Carlo simulation is that where there is more signal, there are more rays. The simulation results in very sharp plots for the image of the parrot, as seen in the resulting bitmap in Figure 3. This image is the product of initially choosing a colorful high-contrast source combined with the algorithm. Figure 3. Left, Original Bitmap; Right, Simulated Image 1 B. Roy Frieden. Probability, Statistical Optics, and Data Testing: A Problem Solving Approach, chapter 7, (Springer Series in Information Sciences, 10), Springer Verlag, February Optical System Image Irradiance Simulations Page 3

4 Compare the bitmap of the parrots in Figure 3 to the bitmap of the Swiss landscape in Figures 4 and 5. Because the original scene in Figure 4 has less contrast and flatter colors, the average number of rays per pixel in the bitmap for Figure 5 is smaller than those in Figure 3. While using a bitmap like the Swiss landscape for a source is possible and perhaps desirable for some modeling questions, more rays would be required. For an image like the parrot, five million rays per color result in an overnight run on a dual Pentium Pro or Pentium II. Figure 4. Original bitmap of Swiss landscape Figure 5. Simulated image of Swiss landscape Optical System Image Irradiance Simulations Page 4

5 Raytracing in ASAP is described by its author, Al Greynolds, as "real world raytracing, which is distinctly different from raytracing in sequential lens design programs". Rather than going in a positive direction to the next element in the system, rays proceed as dictated by the optical properties of the materials they encounter. This process affords an additional dimension to the analysis of systems. The rays we trace through a system interact with all the materials described in the simulation to the degree we choose. Whereas we normally think of irradiance models as the non-imaging evaluation of imaging systems, the simulation here shows the combination of all sorts of effects from cosine to aberrations on a real image. To demonstrate a deleterious effect to a good lens, we have purposely defocused the image of the parrot by 0.2 mm. See Figure 6. Figure 6. Left, original bitmap of parrots; right, simulated image as seen through defocused 0.2 mm lens To create ghosts, the sun was modeled as a collimated beam incident on the first element of the lens with an irradiance that corresponds to the solar constant. A Lambertian emitter was used for the scene, and it was assumed that 10% of the energy that was received from the sun was re-emitted in 2 π steradians. Ghosts are part of stray light radiation, unwanted radiation. We classify stray light into two parts: 1) light that gets to the detector by either bouncing off a mount or the edge of a lens and is called the "unwanted" or "unusual path"; and 2) stray light that propagates by bouncing or reflecting, in accordance with Snell s law or Fresnel reflection, off elements, and these rays are referred to as "ghosts". An even number of bounces is required (two is the minimum) to produce a ghost that reaches the detector. Optical System Image Irradiance Simulations Page 5

6 We can divide ghosts into three classes relative to their path through a system: 1) Ghosts can be produced by sources outside of the field of view that illuminate the first surface and propagate through the system; the most common source is the sun. 2) Ghosts can be created by the secondary effects of rays that pass through the optical system but are not seen by the detector. For example, the image circle of a lens system is not fully utilized by a rectangular detector. The rangefinder, reflex mirror, or detector does not see the source but its effects can nonetheless compromise the final image. 3) Ghosts can be in the field of view. The photographer sees the sun in the viewfinder and can appreciate its effects and proceed or recompose the image. This third class of ghosts can be well modeled in lens design codes and is not covered in this paper. We will model the first two classes of ghosts generated by rays outside the field of view and their effects. These ghosts are problematic for sequential lens design programs. In ghost analysis, the surprises generally come from sources outside the field of view that are much brighter than the scene. Ghosts affect image contrast. Contrast is defined as the maximum energy minus the minimum irradiance value divided by the sum of the two. It is important to note that we are considering the irradiance and not flux, which is the total energy integrated on the detector. The irradiance is the energy-per-unit-area with respect to the eye or detector, and in these simulations it is the relevant measure. We will show that when evaluating systems with out-of-the-field-of-view sources, you can add the energy from the ghost to that of the signal. For any given contrast level in the scene, the effect of ghosts is to raise the DC component so that contrast is reduced. Additionally, with this method we can predict real effects of these ghosts on the final image and recommend prescriptive suggestions for the design in question. The threshold for a viewer to notice the effects of ghosts varies widely. According to a 1980 lens design paper 2, a value as low as 10-6 is sited; but in general, a value of 0.1% or smaller is used when the eye is the detector. If we assume a 1% loss per surface and a 30% reflectivity for the CCD, as in the case of a digital still or video camera, then a value of 1/300 of the signal is typical for an in-field ghost. When the ghost is out of focus, its effect is less significant. For in-field ghosts then, there is little cause for concern from moderate sources. If the photographer wants bright sources such as the sun or street lights in the picture, he or she can weigh the artistic effect and proceed. In anticipation of this, the lens designer can evaluate the potential lens design and choose lens placements, consider the characteristics of the coatings, avoid last surfaces that are concentric with the detector and add baffles as necessary. The approach to baffle or control the out-of-the-field-of-view ghosts can vary. We learned from modeling sources at 22 degrees and 35 degrees in this system that ghosts from the shallow angle have more opportunity to rattle around and degrade the image. See Figures 7 and 8. 2 Tadashi Kojima, et al, "Computer-simulation analysis of ghost images in photographic objectives", SPIE Vol. 237, 1980, International Lens Design Conference (OSA), p Optical System Image Irradiance Simulations Page 6

7 Figure 7. Top, original bitmap of parrots; bottom, inverted mask of 22-degree ghost; middle, combined image Optical System Image Irradiance Simulations Page 7

8 Figure 8. Top, original bitmap of parrots; bottom, inverted mask of 35-degree ghost; middle, combined image From experience we know that the worst candidates for in-field ghosts are the protective windows in front of the CCD. For any ray that reaches the CCD, approximately 30% of the ray will be reflected. Since the protective plates and birefringent crystals are in close proximity to the detector, Optical System Image Irradiance Simulations Page 8

9 the ghosts are not far from focus and can therefore be troublesome for critical users. The recommendation is: if in-field ghosts are a problem for CCD-based systems, then the protective windows are the first place to look and high-quality coatings will be required. For out-of-the-field-of-view-ghosts: the angle of the source of the ghost will predict the area in the system for study. If the ghosts are from sources at narrow angles, either in-field or just slightly out of the field of view, then careful analysis will be required at the rear of the lens. For ghosts coming at steep angles, then the best anti-reflective (AR) coatings will be required at the front of the system. The iris of the system is sometimes visible and considered a distraction; modeling this phenomenon and its effect on the image is now possible. For the iris to be seen at the detector, the ghost must be truncated by the iris or stop. In addition, the even bounce has to occur in front of the stop. For example, in an arbitrary system a ray's first bounce at surface 6 must pass back through the stop at surface 5 and be reflected off surface 4 and ultimately make it back to the detector to be seen. If it is larger than the stop at surface 4 or diverging sufficiently to overfill the iris, then its shape will be seen by the detector. The effect of surface blemishes is difficult to quantify with present tools. This simulation method can yield visual proof of surface roughness, scratches, and pits. At BRO, we utilize BRDF (Bidirectional Reflectance Distribution Function) to characterize surfaces, but this is a difficult measure to visualize. Figure 9 shows the image resulting from a single scratch, 0.1mm wide, that we modeled across the first element. The effect is negligible; however there is no bright source such as the sun modeled, and in that case the results would be much different. Because the effect of the scratch was so unremarkable, it was deepened until its effects were more distinct. Optical System Image Irradiance Simulations Page 9

10 Figure 9. Top, original bitmap of parrots; bottom, 0.1-mm scratch on first element; middle, combined image A 0.4-mm scratch is modeled in Figure 10. Optical System Image Irradiance Simulations Page 10

11 Figure 10. Top, original bitmap of parrots; bottom, 0.4-mm scratch on first element; middle, combined image What is key to this simulation is tracing a large number of rays that is similar to the real process. In the past, when designers wanted an idea of the appearance of the image, they used the object and would convolve it with the point spread function. One method is to start in the Fourier domain and multiply the Fourier transform of the object with the MTF of the lens. Then do the inverse Fourier Optical System Image Irradiance Simulations Page 11

12 transform and obtain the simulation. However, you need to be able to describe the PSF for all the defects we have discussed. Future work will include more detailed modeling of the CCD and the micro lens structures in front of the detector, and their relationships with the lens system. Irradiance modeling, vignetting, and ghosting will be studied. Out-of-focus points sources are also of interest. We predict that we will see the iris shape from out-of-focus sources since the f-number shapes the ray bundles. Our object bitmaps had no depth information, but the simulation can include bitmaps or sources at different locations in object space. The sun s position in the ghost analysis is such a case. The ASAP distribution file is not limited to constructing two dimensional sources. Ray sets may be three-dimensional. This feature has long been used to create volume sources to emulate such phenomena as plasmas. There is also no reason why a bitmap could not be placed on an arbitrary surface from a CAD file and used as an extended source. BRO expects to extend this modeling capability to help designers visualize their work through virtual prototyping. We would like to thank Al Greynolds, Bob Pagano, and Carey Portnoy of BRO for their help. Optical System Image Irradiance Simulations Page 12