Final Project

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Jan 9, 2024

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Optical System Project: The Fingerprint Reader: Lab Exercise #1 – System Layout t1 = 9.423 mm (LED to first face of D1) t2 = 9.779 mm (second face of D1 to first face of D2) t3 = 1.0668 mm (second face of D2 to input face of P1) t4 = 9.017 mm (output face of P1 to input face of P2) t5 = 8.2296 mm (output face of P2 to center of mirror) t6 = 20.9296 mm (center of mirror to center of lens L1) t7 = 1.3716 mm (center of L1 to input face of P3) t8 = 8.382 mm (output face of P3 to input face of P4) t9 = 3.302 mm (output face of P4 to center of lens L2) t10 = 18.8976 mm (center of L2 to the CCD chip image plane) * Use the microscope to measure the dimensions of the CCD chip (the final image plane). Make sure you keep track of which dimension is “Vertical” and which dimension is “Horizontal.” CCD Chip: width= 32.0548 mm x height =32.0294 x depth= 18.034 mm * Make a “2:1 scale” drawing of the entire system.

Lab Exercise #2 – The Fingerprint Image, TIR Goals: * Turn on the power supply and view the output image (prism P1 clean, no fingerprint). Describe what you see. -I see a completely black screen with nothing being illuminated * Place your finger on the prism face and study the output image. Describe what you see. -I see a perfect outline of my fingerprint with the dark parts being my fingerprint and the light parts not being my fingerprint. * Relate both images to actual light in the system.

In the beginning, no light is being reflected back into the system, therefore, the screen appears all black. However, once you put something directly onto the glass, light is then reflected and the system does not appear completely dark anymore. * Use the optical concept of Total Internal Reflection (TIR) to fully explain how the Fingerprint Reader works. Relate your explanation to the output image of your fingerprint that you just observed. -Because the oil on your skin has a larger index of refraction than the glass, TIR occurs on that part of your fingerprint. Consequently, the black lines, or the your fingerprint lines on the reader are the parts of your finger which have these oils and therefore are causing TIR to occur. Thus, the black lines on the reader are the parts of your finger which contain these oils and are exemplifying TIR while the white parts are the parts in which no TIR is occurring at the light is being reflected back into the system. * Based on your observations, how does the value of the refractive index of your skin oil relate to the refractive index of the glass prism -Based on these observations, the refractive index of your skin oil must be greater than the refractive index of the glass prism. Lab Exercise #3 – Unfold the System Goals: - Learn how to ‘unfold’ an optical system about a reflection. - Discover how the object plane is oriented in the Fingerprint Reader. * Use the digital photo from our class website to create a “linear” picture of the system, unfolded about planes of reflection in the system. (Make Xerox copies of your photo, and cut them out to do this.) * How is the object plane oriented with respect to the (unfolded) optical axis? What angle does it make with the optical axis?

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-The object plane is oriented by 90 degrees with respect to the optical axis. Therefore, the object plane makes a 45 degree angle with the optical axis. Lab Exercise #4 – Anamorphic Prism Pair Goals: - Study what the pair of prisms P3 and P4 do in the Fingerprint Reader system. * Measure the ‘magnification’ in the working system (the “anamorphic”effect of P3 and P4). Place a circular object (an o-ring) on the face of (fingerprint) prism P1 and obtain an output image on the LCD screen. Use a ruler to measure the dimensions of the image of the o-ring, on the LCD screen. Now, remove the two prisms and observe what happens to the image. Again, measure the dimensions of the image of the o-ring on the LCD screen. - Fingerprint Reader with P3+P4- 16 cm perfect circle -Fingerprint Reader without p3+p4- ellipse with 16 cm radius in horizontal direction and 12 cm radius in the vertical direction. * Based on your measurements, what does the prism pair do to the image? - does it magnify the minor axis of the ellipse? ... or ... - does it de-magnify the major axis of the ellipse? -Based on these results, the prism pair magnifies the minor axis of the ellipse. * Use your two traces to calculate (quantify) the magnifying effect that the prism pair has on the final image: m (P3, P4) = __________ - m(P3,P4)=16/12=4/3 * Based on the angle that the object (your fingerprint) is tilted with respect to the optical axis, calculate how much the image should be “shrunk” or “fore-shortened” if prisms P3 and P4 are not used: m (due to object tilt) = __________ - m(due to object tilt)= inverse of the magnification= ¾ * Compare these two values of magnification. Do they prove that prisms P3 and P4 compensate for the object tilt? Show your calculations. -m(due to object tilt) *m(P3,P4)= ¾ * 4/3 = 1 Therefore, because these magnifications cancel out to equal one, it is shown that prisms p3 and p4 compensate for object tilt. Lab Exercise #5 – Light Source Uniformity Goals: - Learn about the uniformity of light sources.

- Observe patterns of light from the diffuse light source, that reach the prism face. * Study the distribution of light that is transmitted through just the first diffuser (D1). Make a sketch of what you observe. * Study the distribution of light that is transmitted through just the second diffuser (D2). Make a sketch of what you observe. * Study the distribution of light that is transmitted through both diffusers (D1 and D2). Make a sketch of what you observe. * What seems to be a bigger factor in creating a more uniform distribution of light—placing the diffuser farther away from the LED sources, or using two diffusers “in series”? - Because the light emitting for the diffusers in series is a lot less dim than the light emitted from the 2 nd diffuser, we can assert that using two diffusers (in series) is a bigger factor in creating a more uniform distribution of light. Lab Exercise #6 – Focal Lengths of the Lenses Goals: - Measure the focal lengths of both lenses. - Calculate their F/#’s. * Use the setup provided to measure the focal length of both lenses. To simplify things, we will treat them as being “thin lenses”, and measure from the nominal center of each lens to the focal point: f.l. (L1) = 185 mm

f.l. (L2) = 145 mm * Using your values for lens diameters that you took in Lab Exercise #1, calculate the F/# of each lens: F/# (L1) = 14.08 F/# (L2) = 31.52 Work: Lab Exercise #7 – Gaussian Reduction Goals: - Gaussian reduce lenses L1 and L2 into one pair of principal planes. - Compare the calculated image magnification to what you measure for the system. - Study the effects of the prisms on system magnification. * Based on all of your measured data so far, calculate the location of the Gaussian- reduced principal planes for L1 and L2. Refer your values to the center of L1. * Using the location of these “system” principal planes, what is the object distance?

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(ignore the added path length due to any intervening glass) z = -45.79674 mm * Using the location of these “system” principal planes, what is the image distance? (ignore the added path length due to any intervening glass) z′ = 24.870 mm * Calculate the transverse magnification of the system using these values: Transverse Magnification= -0.54306 Work:

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