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

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

Answer 1

[John BG]

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 2−y2 5222xy 621 −2x+3xHx2+y2L 721 −2y+3yHx2+y2L 8201 −6Hx2+y2L+6Hx2+y2L2 933x 3−3xy 2 10333x2y−y3 1132−3x 2+3y 2+4x 2Hx2+y2L−4y 2Hx2+y2L 1232 −6xy+8xyHx2+y2L 13313x −12xHx2+y2L+10xHx2+y2L2 14313y −12yHx2+y2L+10yHx2+y2L2 1530 −1+12Hx2+y2L−30Hx2+y2L2+20Hx2+y2L3 1644x 4−6x 2y2+y4 17444x3y−4xy 3 1843−4x 3+12xy2+5x 3Hx2+y2L−15xy2Hx2+y2L 1943 −12x2y+4y 3+15x2yHx2+y2L−5y 3Hx2+y2L 20426x 2−6y 2−20x2Hx2+y2L+20y2Hx2+y2L+15x2Hx2+y2L2−15y2Hx2+y2L2 214212xy −40xyHx2+y2L+30xyHx2+y2L2 2241 −4x+30xHx2+y2L−60xHx2+y2L2+35xHx2+y2L3 2341 −4y+30yHx2+y2L−60yHx2+y2L2+35yHx2+y2L3 24401 −20Hx2+y2L+90Hx2+y2L2−140Hx2+y2L3+70Hx2+y2L4 2555x 5−10x3y2+5xy 4 26555x4y−10x2y3+y5 2754−5x 4+30x2y2−5y 4+6x 4Hx2+y2L−36x2y2Hx2+y2L+6y 4Hx2+y2L 2854 −20x3y+20xy3+24x3yHx2+y2L−24xy3Hx2+y2L 295310x 3−30xy2−30x3Hx2+y2L+90xy2Hx2+y2L+21x3Hx2+y2L2−63xy2Hx2+y2L2 305330x 2y−10y3−90x2yHx2+y2L+30y3Hx2+y2L+63x2yHx2+y2L2−21y3Hx2+y2L2 3152 −10x2+10y2+60x2Hx2+y2L−60y2Hx2+y2L−105x2Hx2+y2L2+105y2Hx2+y2L2+56x2Hx2+y2L3−56y2Hx2+y2L3 3252 −20xy+120xyHx2+y2L−210xyHx2+y2L2+112xyHx2+y2L3 33515x −60xHx2+y2L+210xHx2+y2L2−280xHx2+y2L3+126xHx2+y2L4 34515y −60yHx2+y2L+210yHx2+y2L2−280yHx2+y2L3+126yHx2+y2L4 3550 −1+30Hx2+y2L−210Hx2+y2L2+560Hx2+y2L3−630Hx2+y2L4+252Hx2+y2L5 3666x 6−15x4y2+15x2y4−y6 37666x5y−20x3y3+6xy 5 3865−6x 5+60x3y2−30xy4+7x 5Hx2+y2L−70x3y2Hx2+y2L+35xy4Hx2+y2L 3965 −30x4y+60x2y3−6y 5+35x4yHx2+y2L−70x2y3Hx2+y2L+7y 5Hx2+y2L 406415x 4−90x2y2+15y4−42x4Hx2+y2L+252x2y2Hx2+y2L−42y4Hx2+y2L+28x4Hx2+y2L2−168x2y2Hx2+y2L2+28y4Hx2+y2L2
416460x3y−60xy3−168x3yHx2+y2L+168xy3Hx2+y2L+112x3yHx2+y2L2−112xy3Hx2+y2L2 4263−20x3+60xy2+105x3Hx2+y2L−315xy2Hx2+y2L−168x3Hx2+y2L2+504xy2Hx2+y2L2+84x3Hx2+y2L3−252xy2Hx2+y2L3 4363−60x2y+20y3+315x2yHx2+y2L−105y3Hx2+y2L−504x2yHx2+y2L2+168y3Hx2+y2L2+252x2yHx2+y2L3−84y3Hx2+y2L3 446215x2−15y2−140x2Hx2+y2L+140y2Hx2+y2L+420x2Hx2+y2L2−420y2Hx2+y2L2−504x2Hx2+y2L3+504y2Hx2+y2L3+210x2Hx2+y2L4−210y2Hx2+y2L4 456230xy−280xyHx2+y2L+840xyHx2+y2L2−1008xyHx2+y2L3+420xyHx2+y2L4 4661−6x+105xHx2+y2L−560xHx2+y2L2+1260xHx2+y2L3−1260xHx2+y2L4+462xHx2+y2L5 4761−6y+105yHx2+y2L−560yHx2+y2L2+1260yHx2+y2L3−1260yHx2+y2L4+462yHx2+y2L5 48601−42Hx2+y2L+420Hx2+y2L2−1680Hx2+y2L3+3150Hx2+y2L4−2772Hx2+y2L5+924Hx2+y2L6