# Singlet lens imaging Optical raytracing design and experimental by mifei

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```									Singlet lens imaging: Optical raytracing design and experimental characterization The goal is to design an imaging system with -10x magnification and the best possible resolution, using only a single refractive lens (a „singlet‟) with a 100mm focal lengthand a 50mm lens diameter. First, calculate the paraxial object and image plane for this system using the lensmaker‟s formula (1/o + 1/i = 1/f) for -10x magnification and f==100mm. What are the object and image distances? In paraxial imaging, and assuming a thin lens, this system is now fully defined. However, Zemax raytracing makes fewer approximations and will show you that there is still an important degree of freedom: the curvature of each side of the singlet lens. The drawing below illustrates “lens bending” where the same total thickness of the lens is maintained as the optical power is moved between the front and back surfaces of the lens. With a thin lens approximation, all these lenses are identical. In practice these lenses have very different aberrations, and may be better suited to accomplish specific imaging goals.
Meniscus Plano-Convex Bi-Convex Plano-Convex Meniscus

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For our example we will use BK7 (a common glass used in optics) as the lens material and a single 500 nm (green) wavelength for our illumination and a 10 mm thick lens. In Zemax, set up the imaging system with the object and image distances you calculated and a plano-convex lens with the curved side closer to the object. Use “layout” to see your system. Set up the object as a point source on axis, and adjust the lens curvature to achieve approximate imaging. Use your merit function to optimize the lens, and record the value of the merit function achieved. Record the curvature, and take an image file of

the lens. Now generate a through-focus spot diagram, using a random ray pattern, and setting the spacing between focus points to allow you to see the point blurring by at least twice the smallest diameter. What is the approximate spot size? Record the throughfocus spot diagram as an image file. Now take the lens and reverse its position using the “reverse elements” function. Keeping the total separation between the object and image plane constant, adjust the lens position to achieve best focus. Record the merit function achieved, take an image of the new lens layout, and repeat the through-focus spot diagram. What is the approximate spot size? Finally, repeat this process with a symmetric bi-convex lens with total thickness 10mm (have your TA show you how to use „pick up‟ to automatically make the curvatures equal). Repeat the optimization, and record the merit function achieved, the lens layout, and through focus spot diagrams. What is the approximate spot size? Based on these designs, you should be able to pick which of the three lens arrangements will produce the best image. Now we will test this prediction on the optical bench. We will use BK7 100 mm focal length lenses that are plano-convex and bi-spheric, which should be almost identical to the lenses which you have designed. Set up a resolution target with diffuse illumination and an image plane at the calculated distance from the object. Place a paper screen at the image plane so you can see the magnified and inverted image. Place the plano-convex lens between the object and image and adjust the position until you have the best image. Photograph the entire image using a digital camera. Repeat this process with the lens reversed, then with the symmetric biconvex lens. Which lens arrangement produces the best overall image? Now repeat this process using a CCD sensor at the image plane to examine the fine resolution at the center of the image. Which lens arrangement produces the best resolution? Finally, using the WORST lens arrangement, look at the effect of placing an iris near the lens to restrict the lens to 1/5 it‟s original diameter (10 mm). Does the performance improve, for either the fine resolution (on the CCD) or the overall image (on the screen)? Why? Slide the aperture to the side of the lens, so that you are using only the edge area of the lens aperture. What is the effect on the imaging performance? Why?

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