Human Optics as a Function of Eccentricity - Revision history

imported>Student2018: /* Appendix II */

2018-12-15T02:38:18Z

Appendix II

← Older revision		Revision as of 02:38, 15 December 2018
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	''Nicholas Gaudio'' - Conceptualized the algorithm and plots. Wrote the methods, results, and conclusion of the report and presentation. Compared the ISET results to the publication results.		''Nicholas Gaudio'' - Conceptualized the algorithm and plots. Wrote the methods, results, and conclusion of the report and presentation. Compared the ISET results to the publication results.

	''Paavani Dua'' - ~~Read~~ the literature understanding and wrote introduction and background of the report.		''Paavani Dua'' - Lead the literature understanding and wrote introduction and background of the report.

imported>Student2018 at 02:36, 15 December 2018

2018-12-15T02:36:11Z

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	<div style="text-align: center;"> '''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].'' </div>		<div style="text-align: center;"> '''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].'' </div>

	From the comparison between the ISET Navarro model simulations and the publication as shown in Figure 11, similar trends were seen between the corresponding eccentricity values such that the larger the eccentricity, the faster the MTF plot ~~descented~~ for both the ISET and publication results. However, the MTF50 values for the ISET results were all at lower spatial frequencies compared to the publication.		From the comparison between the ISET Navarro model simulations and the publication as shown in Figure 10, similar trends were seen between the corresponding eccentricity values such that the larger the eccentricity, the faster the MTF plot descended for both the ISET and publication results. However, the MTF50 values for the ISET results were all at lower spatial frequencies compared to the publication.

	== Conclusions ==		== Conclusions ==

imported>Student2018: /* Methods */

2018-12-15T02:34:24Z

Methods

← Older revision		Revision as of 02:34, 15 December 2018
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	and use this value as the relative field of view:		and use this value as the relative field of view:

	<div style="text-align: center;"> <math>~~relative_degree~~ = \frac{r}{LOWRES * FOV}</math> </div>		<div style="text-align: center;"> <math>relative degree = \frac{r}{LOWRES * FOV}</math> </div>

	We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).		We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).

imported>Student2018: /* Methods */

2018-12-15T02:34:08Z

Methods

← Older revision		Revision as of 02:34, 15 December 2018
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	and use this value as the relative field of view:		and use this value as the relative field of view:

	<div style="text-align: center;"> <math>~~relative degree~~ = \frac{r}{LOWRES * FOV}</math> </div>		<div style="text-align: center;"> <math>relative_degree = \frac{r}{LOWRES * FOV}</math> </div>

	We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).		We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).

imported>Student2018 at 02:33, 15 December 2018

2018-12-15T02:33:14Z

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	Several schematic eye models have been compared in literature to the data from real eyes to assess their relative utility with metrics such as their wavefront aberrations, image quality metrics and peripheral refraction profiles. The Navarro eye model is of particular interest in this project. The following figures are from the Williams[4] paper, and are the known results for the Navarro eye model from literature which will be compared to our results.		Several schematic eye models have been compared in literature to the data from real eyes to assess their relative utility with metrics such as their wavefront aberrations, image quality metrics and peripheral refraction profiles. The Navarro eye model is of particular interest in this project. The following figures are from the Williams[4] paper, and are the known results for the Navarro eye model from literature which will be compared to our results.

	[[File:nsgFig1.png \|400 px]]		<div style="text-align: center;"> [[File:nsgFig1.png \|400 px]] </div>

	'''''Figure 1:''' MTFs at eccentricities 0, 10, 20 and 40 deg for an average optical quality of the eye in the horizontal meridian of the temporal retina.''		<div style="text-align: center;"> '''''Figure 1:''' MTFs at eccentricities 0, 10, 20 and 40 deg for an average optical quality of the eye in the horizontal meridian of the temporal retina.'' </div>

	[[File:nsgFig2.png \|400 px]]		<div style="text-align: center;"> [[File:nsgFig2.png \|400 px]] </div>

	'''''Figure 2:''' MTFs at eccentricities 0, 10, 20 and 40 deg for an average optical quality of the eye at the tangential and sagittal focii of the temporal retina.''		<div style="text-align: center;"> '''''Figure 2:''' MTFs at eccentricities 0, 10, 20 and 40 deg for an average optical quality of the eye at the tangential and sagittal focii of the temporal retina.'' </div>

	The slant edge target is used as the test scene. It is the optical equivalent of an electrical step function. The illuminance plot of the test scene across the boundary is the edge spread function, and its Fourier transform is the Modulation Transfer Function. Effective resolution of the lens is greater due to slant since spacing of “samples” of ESF is calculated as pixel pitch times the angle of rotation of the target[3].		The slant edge target is used as the test scene. It is the optical equivalent of an electrical step function. The illuminance plot of the test scene across the boundary is the edge spread function, and its Fourier transform is the Modulation Transfer Function. Effective resolution of the lens is greater due to slant since spacing of “samples” of ESF is calculated as pixel pitch times the angle of rotation of the target[3].
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	The user selected input to the function is the retinal region of interest in units of degrees relative to the fovea (in both the x and y direction) and the crop-window resolution. The hard-coded parameters of the algorithm are FOV4MTF which determines the number of degrees each crop-window spans, and LOW_RES which is the low resolution of the entire FOV image to locate the crop windows off of. It was determined that a crop-window of 2 degrees contained enough information and the entire blurred edge even at eccentricities of 30 degrees as seen in Figure 3.		The user selected input to the function is the retinal region of interest in units of degrees relative to the fovea (in both the x and y direction) and the crop-window resolution. The hard-coded parameters of the algorithm are FOV4MTF which determines the number of degrees each crop-window spans, and LOW_RES which is the low resolution of the entire FOV image to locate the crop windows off of. It was determined that a crop-window of 2 degrees contained enough information and the entire blurred edge even at eccentricities of 30 degrees as seen in Figure 3.

	[[File:nsgFig3.png \|600 px]]		<div style="text-align: center;"> [[File:nsgFig3.png \|600 px]] </div>

	'''''Figure 3:''' A crop-window at an eccentricity of 0 and 30 degrees.		<div style="text-align: center;"> '''''Figure 3:''' A crop-window at an eccentricity of 0 and 30 degrees.'' </div>
	''

	Similarly, our crop-window solution requires a whole scene render with a lower resolution first. A resolution of 100 was determined to be a reasonable choice since the data of row numbers and column numbers for setting the cropwindow parameter in sceneEye is normalized. Thus, a 2 digit of accuracy is enough.		Similarly, our crop-window solution requires a whole scene render with a lower resolution first. A resolution of 100 was determined to be a reasonable choice since the data of row numbers and column numbers for setting the cropwindow parameter in sceneEye is normalized. Thus, a 2 digit of accuracy is enough.

	[[File:nsgFig4.png \|800 px]]		<div style="text-align: center;"> [[File:nsgFig4.png \|800 px]] </div>

	'''''Figure 4:''' ROI and crop-window comparisons for FOV values of 1, 15, and 30 degrees.''		<div style="text-align: center;"> '''''Figure 4:''' ROI and crop-window comparisons for FOV values of 1, 15, and 30 degrees.'' </div>

	All of the crop-windows must contain a slanted edge to calculate the MTF at said eccentricity. Even though the slanted bar only appears in some parts of the retinal rendered image, the user can input regions of interest that don’t contain the edge of the slanted edge scene at all. This is due to the fact that the Navarro eye model in ISET is radially symmetric. Leveraging this symmetry, it is permissible to transform the user-input to an equivalent position containing a slanted edge to successfully calculate the MTF at the crop-window’s radial distance as seen in Figure 4. The method is to calculate the radial distance from the fovea of the x, y coordinates:		All of the crop-windows must contain a slanted edge to calculate the MTF at said eccentricity. Even though the slanted bar only appears in some parts of the retinal rendered image, the user can input regions of interest that don’t contain the edge of the slanted edge scene at all. This is due to the fact that the Navarro eye model in ISET is radially symmetric. Leveraging this symmetry, it is permissible to transform the user-input to an equivalent position containing a slanted edge to successfully calculate the MTF at the crop-window’s radial distance as seen in Figure 4. The method is to calculate the radial distance from the fovea of the x, y coordinates:
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	and use this value as the relative field of view:		and use this value as the relative field of view:

	<div style="text-align: center;"> <math>relative degree = \frac{r}{LOWRES * FOV}</math> </div>		<div style="text-align: center;"> <math>relative degree = \frac{r}{LOWRES * FOV}</math> </div>

	We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).		We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).

	[[File:nsgFig5.png \|800 px]]		<div style="text-align: center;"> [[File:nsgFig5.png \|800 px]] </div>

	'''''Figure 5:''' ROI and crop-window comparisons for off-center ROIs.''		<div style="text-align: center;"> '''''Figure 5:''' ROI and crop-window comparisons for off-center ROIs.'' </div>

	The automation of properly placing the crop-windows has to be done row by row because when FOV is large, the scene will be distorted and slanted bar is no longer a straight line due to the off-axis optical properties of eye. Figure 4 shows these optical effects when the field of view is 30 degrees. The crop-windows are determined by finding the first column in the respective row where the value is nonzero. Then the window is shifted left ⅓ its width so that the slanted bar will not be at the edge of the crop-window, allowing for the while blurred edge to in the crop-window. Then, the next crop-window is located by shifting downward by the size of a crop-window and finding the new nonzero column number. Again, this loop continues until the center of the image is reached or the radius of interest is left.		The automation of properly placing the crop-windows has to be done row by row because when FOV is large, the scene will be distorted and slanted bar is no longer a straight line due to the off-axis optical properties of eye. Figure 4 shows these optical effects when the field of view is 30 degrees. The crop-windows are determined by finding the first column in the respective row where the value is nonzero. Then the window is shifted left ⅓ its width so that the slanted bar will not be at the edge of the crop-window, allowing for the while blurred edge to in the crop-window. Then, the next crop-window is located by shifting downward by the size of a crop-window and finding the new nonzero column number. Again, this loop continues until the center of the image is reached or the radius of interest is left.
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	The first diagnostic test was a sanity check. Figure 6 shows that as the eccentricity increased, the contrast reduction was of a greater value. This response is of expected behavior. It can also be seen that the MTF traces followed expected trends satisfying the sanity check. Figure 7 shows the MTF50 spatial frequencies for the same eccentricities of the same simulation, also following the expected trend.		The first diagnostic test was a sanity check. Figure 6 shows that as the eccentricity increased, the contrast reduction was of a greater value. This response is of expected behavior. It can also be seen that the MTF traces followed expected trends satisfying the sanity check. Figure 7 shows the MTF50 spatial frequencies for the same eccentricities of the same simulation, also following the expected trend.

	[[File:nsgFig6.png \|800 px]]		<div style="text-align: center;"> [[File:nsgFig6.png \|800 px]] </div>

	'''''Figure 6:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 1, pupil diameter = 4 mm, CA Bands = 1, Rays = 64.''		<div style="text-align: center;"> '''''Figure 6:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 1, pupil diameter = 4 mm, CA Bands = 1, Rays = 64.'' </div>

	[[File:nsgFig7.png \|400 px]]		<div style="text-align: center;"> [[File:nsgFig7.png \|400 px]] </div>

	'''''Figure 7:''' MTF50 plot at different eccentricities with crop window resolution = 800, accommodation = 1, pupil diameter = 4 mm, CA Bands = 1, Rays = 64.''		<div style="text-align: center;"> '''''Figure 7:''' MTF50 plot at different eccentricities with crop window resolution = 800, accommodation = 1, pupil diameter = 4 mm, CA Bands = 1, Rays = 64.'' </div>

	Having the sanity check completed, the parameters were set to the parameters used in the William’s[4] paper. It is to be noted that a low ray number was used to reduce computation time in forming the plots. It is suggested that that ray number be increased to 4,000 from the current 128 for future tests. The results can be seen in Figure 8 and Figure 9. The MTF trends with the parameters in the publication still follow expected behavior.		Having the sanity check completed, the parameters were set to the parameters used in the William’s[4] paper. It is to be noted that a low ray number was used to reduce computation time in forming the plots. It is suggested that that ray number be increased to 4,000 from the current 128 for future tests. The results can be seen in Figure 8 and Figure 9. The MTF trends with the parameters in the publication still follow expected behavior.

	[[File:nsgFig8.png \|800 px]]		<div style="text-align: center;"> [[File:nsgFig8.png \|800 px]] </div>

	'''''Figure 8:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.''		<div style="text-align: center;"> '''''Figure 8:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.'' </div>

	[[File:nsgFig9.png \|400 px]]		<div style="text-align: center;"> [[File:nsgFig9.png \|400 px]] </div>

	'''''Figure 9:''' MTF50 plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.''		<div style="text-align: center;"> '''''Figure 9:''' MTF50 plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.'' </div>

	[[File:nsgFig10.png \|800 px]]		<div style="text-align: center;"> [[File:nsgFig10.png \|800 px]] </div>

	'''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].''		<div style="text-align: center;"> '''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].'' </div>

	From the comparison between the ISET Navarro model simulations and the publication as shown in Figure 11, similar trends were seen between the corresponding eccentricity values such that the larger the eccentricity, the faster the MTF plot descented for both the ISET and publication results. However, the MTF50 values for the ISET results were all at lower spatial frequencies compared to the publication.		From the comparison between the ISET Navarro model simulations and the publication as shown in Figure 11, similar trends were seen between the corresponding eccentricity values such that the larger the eccentricity, the faster the MTF plot descented for both the ISET and publication results. However, the MTF50 values for the ISET results were all at lower spatial frequencies compared to the publication.

imported>Student2018: /* Methods */

2018-12-15T02:30:54Z

Methods

← Older revision		Revision as of 02:30, 15 December 2018
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	and use this value as the relative field of view:		and use this value as the relative field of view:

	<math>relative degree = \frac{r}{LOWRES * FOV}</math>		<div style="text-align: center;"> <math>relative degree = \frac{r}{LOWRES * FOV}</math> </div>

	We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).		We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).

imported>Student2018: /* Methods */

2018-12-15T02:30:15Z

Methods

← Older revision		Revision as of 02:30, 15 December 2018
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	<math>r = \sqrt{x^2 + y^2}</math>		<div style="text-align: center;"> <math>r = \sqrt{x^2 + y^2}</math> </div>

	and use this value as the relative field of view:		and use this value as the relative field of view:

imported>Student2018 at 02:29, 15 December 2018

2018-12-15T02:29:38Z

← Older revision		Revision as of 02:29, 15 December 2018
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	The user selected input to the function is the retinal region of interest in units of degrees relative to the fovea (in both the x and y direction) and the crop-window resolution. The hard-coded parameters of the algorithm are FOV4MTF which determines the number of degrees each crop-window spans, and LOW_RES which is the low resolution of the entire FOV image to locate the crop windows off of. It was determined that a crop-window of 2 degrees contained enough information and the entire blurred edge even at eccentricities of 30 degrees as seen in Figure 3.		The user selected input to the function is the retinal region of interest in units of degrees relative to the fovea (in both the x and y direction) and the crop-window resolution. The hard-coded parameters of the algorithm are FOV4MTF which determines the number of degrees each crop-window spans, and LOW_RES which is the low resolution of the entire FOV image to locate the crop windows off of. It was determined that a crop-window of 2 degrees contained enough information and the entire blurred edge even at eccentricities of 30 degrees as seen in Figure 3.

	[[File:nsgFig3.png \|~~400~~ px]]		[[File:nsgFig3.png \|600 px]]

	'''''Figure 3:''' A crop-window at an eccentricity of 0 and 30 degrees.		'''''Figure 3:''' A crop-window at an eccentricity of 0 and 30 degrees.

imported>Student2018 at 02:29, 15 December 2018

2018-12-15T02:29:04Z

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	Similarly, our crop-window solution requires a whole scene render with a lower resolution first. A resolution of 100 was determined to be a reasonable choice since the data of row numbers and column numbers for setting the cropwindow parameter in sceneEye is normalized. Thus, a 2 digit of accuracy is enough.		Similarly, our crop-window solution requires a whole scene render with a lower resolution first. A resolution of 100 was determined to be a reasonable choice since the data of row numbers and column numbers for setting the cropwindow parameter in sceneEye is normalized. Thus, a 2 digit of accuracy is enough.

	[[File:nsgFig4.png \|~~400~~ px]]		[[File:nsgFig4.png \|800 px]]

	'''''Figure 4:''' ROI and crop-window comparisons for FOV values of 1, 15, and 30 degrees.''		'''''Figure 4:''' ROI and crop-window comparisons for FOV values of 1, 15, and 30 degrees.''
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	We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).		We calculate the closest point from the user inputed region of interest (the green box) to the center of the first crop-window. This looped process ensues until our automation algorithm exceeds the region of interest, where the loop terminates. This performance can be seen in Figure 5 where the region of interest does not go though (0, 0).

	[[File:nsgFig5.png \|~~400~~ px]]		[[File:nsgFig5.png \|800 px]]

	'''''Figure 5:''' ROI and crop-window comparisons for off-center ROIs.''		'''''Figure 5:''' ROI and crop-window comparisons for off-center ROIs.''
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	The first diagnostic test was a sanity check. Figure 6 shows that as the eccentricity increased, the contrast reduction was of a greater value. This response is of expected behavior. It can also be seen that the MTF traces followed expected trends satisfying the sanity check. Figure 7 shows the MTF50 spatial frequencies for the same eccentricities of the same simulation, also following the expected trend.		The first diagnostic test was a sanity check. Figure 6 shows that as the eccentricity increased, the contrast reduction was of a greater value. This response is of expected behavior. It can also be seen that the MTF traces followed expected trends satisfying the sanity check. Figure 7 shows the MTF50 spatial frequencies for the same eccentricities of the same simulation, also following the expected trend.

	[[File:nsgFig6.png \|~~400~~ px]]		[[File:nsgFig6.png \|800 px]]

	'''''Figure 6:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 1, pupil diameter = 4 mm, CA Bands = 1, Rays = 64.''		'''''Figure 6:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 1, pupil diameter = 4 mm, CA Bands = 1, Rays = 64.''
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	Having the sanity check completed, the parameters were set to the parameters used in the William’s[4] paper. It is to be noted that a low ray number was used to reduce computation time in forming the plots. It is suggested that that ray number be increased to 4,000 from the current 128 for future tests. The results can be seen in Figure 8 and Figure 9. The MTF trends with the parameters in the publication still follow expected behavior.		Having the sanity check completed, the parameters were set to the parameters used in the William’s[4] paper. It is to be noted that a low ray number was used to reduce computation time in forming the plots. It is suggested that that ray number be increased to 4,000 from the current 128 for future tests. The results can be seen in Figure 8 and Figure 9. The MTF trends with the parameters in the publication still follow expected behavior.

	[[File:nsgFig8.png \|~~400~~ px]]		[[File:nsgFig8.png \|800 px]]

	'''''Figure 8:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.''		'''''Figure 8:''' MTF plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.''
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	'''''Figure 9:''' MTF50 plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.''		'''''Figure 9:''' MTF50 plot at different eccentricities with crop window resolution = 800, accommodation = 0.33, pupil diameter = 3 mm, CA Bands = 8, Rays = 128.''

	[[File:nsgFig10.png \|~~400~~ px]]		[[File:nsgFig10.png \|800 px]]

	'''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].''		'''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].''

imported>Student2018 at 02:28, 15 December 2018

2018-12-15T02:28:22Z

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	[[File:nsgFig10.png \|400 px]]		[[File:nsgFig10.png \|400 px]]

	'''''Figure 11:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].''		'''''Figure 10:''' MTF plot at different eccentricities comparing the ISET results to the Williams publication results[4].''

	From the comparison between the ISET Navarro model simulations and the publication as shown in Figure 11, similar trends were seen between the corresponding eccentricity values such that the larger the eccentricity, the faster the MTF plot descented for both the ISET and publication results. However, the MTF50 values for the ISET results were all at lower spatial frequencies compared to the publication.		From the comparison between the ISET Navarro model simulations and the publication as shown in Figure 11, similar trends were seen between the corresponding eccentricity values such that the larger the eccentricity, the faster the MTF plot descented for both the ISET and publication results. However, the MTF50 values for the ISET results were all at lower spatial frequencies compared to the publication.