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Converting from Zernike's Polynomials values to a Point Spread and Modulation Transfer Function

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Dear all,
I have a dataset obtained from a wavefront sensor that provides me with the values of the first 36 Zernike's Polynomials for many research subjects. I would like to derive both the point spread function (PSF) and modulation transfer function (MTF) from these data, similar to what is shown here. The PSF is especially important.
Is there any set of tools for MATLAB that will make this feasible? I am not an expert in optics.
Sincerely, Jim

Respuesta aceptada

John BG
John BG el 28 de Oct. de 2015
To operate the instrument, read the manual: If you play a bit with the boxes of the link you include as 'here', one at a time, start with #1:1 and the rest 0, then #1:0 #2:1 rest zero and so on, you realize that #1 #2 #3 ... are the indices the indexes of Zernike equations as listed in http://fp.optics.arizona.edu/jcwyant/Zernikes/ZernikeEquations.htm PSF and MTF are just 3D plots, the term 'Irradiance' shows up, but you just have to solve each equation reading the numeral #I on the left of the table for [ro theta_x and theta_y]. Mind the gap the previous link showing the equations names theta, both theta_x and theta_y, but the far right column helps tell. Copied the table that shows x and y, as theta_x and theta_y below these lines, Courtesy of ZernikePolynomialsForTheWeb.nbJames C. Wyant, 20035.
Hope it helps
John
#nmPolynomial 0001 111x 211y 310 1+2Hx2+y2L 422x 2y2 5222xy 621 2x+3xHx2+y2L 721 2y+3yHx2+y2L 8201 6Hx2+y2L+6Hx2+y2L2 933x 33xy 2 10333x2yy3 11323x 2+3y 2+4x 2Hx2+y2L4y 2Hx2+y2L 1232 6xy+8xyHx2+y2L 13313x 12xHx2+y2L+10xHx2+y2L2 14313y 12yHx2+y2L+10yHx2+y2L2 1530 1+12Hx2+y2L30Hx2+y2L2+20Hx2+y2L3 1644x 46x 2y2+y4 17444x3y4xy 3 18434x 3+12xy2+5x 3Hx2+y2L15xy2Hx2+y2L 1943 12x2y+4y 3+15x2yHx2+y2L5y 3Hx2+y2L 20426x 26y 220x2Hx2+y2L+20y2Hx2+y2L+15x2Hx2+y2L215y2Hx2+y2L2 214212xy 40xyHx2+y2L+30xyHx2+y2L2 2241 4x+30xHx2+y2L60xHx2+y2L2+35xHx2+y2L3 2341 4y+30yHx2+y2L60yHx2+y2L2+35yHx2+y2L3 24401 20Hx2+y2L+90Hx2+y2L2140Hx2+y2L3+70Hx2+y2L4 2555x 510x3y2+5xy 4 26555x4y10x2y3+y5 27545x 4+30x2y25y 4+6x 4Hx2+y2L36x2y2Hx2+y2L+6y 4Hx2+y2L 2854 20x3y+20xy3+24x3yHx2+y2L24xy3Hx2+y2L 295310x 330xy230x3Hx2+y2L+90xy2Hx2+y2L+21x3Hx2+y2L263xy2Hx2+y2L2 305330x 2y10y390x2yHx2+y2L+30y3Hx2+y2L+63x2yHx2+y2L221y3Hx2+y2L2 3152 10x2+10y2+60x2Hx2+y2L60y2Hx2+y2L105x2Hx2+y2L2+105y2Hx2+y2L2+56x2Hx2+y2L356y2Hx2+y2L3 3252 20xy+120xyHx2+y2L210xyHx2+y2L2+112xyHx2+y2L3 33515x 60xHx2+y2L+210xHx2+y2L2280xHx2+y2L3+126xHx2+y2L4 34515y 60yHx2+y2L+210yHx2+y2L2280yHx2+y2L3+126yHx2+y2L4 3550 1+30Hx2+y2L210Hx2+y2L2+560Hx2+y2L3630Hx2+y2L4+252Hx2+y2L5 3666x 615x4y2+15x2y4y6 37666x5y20x3y3+6xy 5 38656x 5+60x3y230xy4+7x 5Hx2+y2L70x3y2Hx2+y2L+35xy4Hx2+y2L 3965 30x4y+60x2y36y 5+35x4yHx2+y2L70x2y3Hx2+y2L+7y 5Hx2+y2L 406415x 490x2y2+15y442x4Hx2+y2L+252x2y2Hx2+y2L42y4Hx2+y2L+28x4Hx2+y2L2168x2y2Hx2+y2L2+28y4Hx2+y2L2
416460x3y60xy3168x3yHx2+y2L+168xy3Hx2+y2L+112x3yHx2+y2L2112xy3Hx2+y2L2 426320x3+60xy2+105x3Hx2+y2L315xy2Hx2+y2L168x3Hx2+y2L2+504xy2Hx2+y2L2+84x3Hx2+y2L3252xy2Hx2+y2L3 436360x2y+20y3+315x2yHx2+y2L105y3Hx2+y2L504x2yHx2+y2L2+168y3Hx2+y2L2+252x2yHx2+y2L384y3Hx2+y2L3 446215x215y2140x2Hx2+y2L+140y2Hx2+y2L+420x2Hx2+y2L2420y2Hx2+y2L2504x2Hx2+y2L3+504y2Hx2+y2L3+210x2Hx2+y2L4210y2Hx2+y2L4 456230xy280xyHx2+y2L+840xyHx2+y2L21008xyHx2+y2L3+420xyHx2+y2L4 46616x+105xHx2+y2L560xHx2+y2L2+1260xHx2+y2L31260xHx2+y2L4+462xHx2+y2L5 47616y+105yHx2+y2L560yHx2+y2L2+1260yHx2+y2L31260yHx2+y2L4+462yHx2+y2L5 4860142Hx2+y2L+420Hx2+y2L21680Hx2+y2L3+3150Hx2+y2L42772Hx2+y2L5+924Hx2+y2L6

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