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Note that n/W now represents a spatial frequency (e.g. cycles per unit length). <@HJ8$In the optical domain, the spatial radian frequency is #)  The scaled FFT is then   What this means is that for FFT output representing angular direction (in radians) the FFT should have its coordinate wave scaling set from  assuming that the centering mode convention for the FFT output is used when calculating the FFT. Note that MatrixOP (rather than the FFT operation) may be used for faster calculations of FFTs.  If the final result is desired as a physical lateral distance perpendicular to the propagation axis, the previous scaling limits should be mutiplied by the appropriate propagation distance.  w For a far-field pattern, that propagation distance is the range R from the source field location and the scaling is:   nFor a focus of a paraxial lens, that propagation distance is the focal length of the lens and the scaling is:  To avoid confusion and mistakes, it is recommended that all physical lengths be expressed using a common dimension (e.g. "m", for meters). This allows graph axes to be labled (with scaled exponents) automatically.  $ Fourier Optics - Code Example (Hfunction Test() // assumes 512x512 data H 4H variable W = 25.4e-2 // source plane dimension, m (H variable a = 12.7e-3 // lens radius, m -H variable fL = 30e-3 // lens focal length, m .H variable lambda = 1.54e-6 // wavelength , m H make/O/C/N=(512,512) wave0 "H setscale x, -W/2, W/2, "m" wave0 "H setscale y, -W/2, W/2, "m" wave0 <H wave0 = cmplx( 1*((x^2+y^2)=a^2), 0 ) 4H FFT/OUT=3/DEST=wave0_FFT wave0 // magnitude output YH setscale x, -lambda*fL*256/W, lambda*fL*256/W,"m" wave0_FFT // optical scaling at focus =H setscale y, -lambda*fL*256/W, lambda*fL*256/W,"m" wave0_FFT H GH Make/O/n=2 xTrace={ -lambda*fL*256/W, lambda*fL*256/W} ,yTrace={0, 0} @H ImageLineProfile srcWave=wave0_FFT, xWave=xTrace, yWave=yTrace 'H SetScale d, 1e-6, 2e-6 , "m", yTrace 'H SetScale d, 1e-6, 2e-6 , "m", xTrace H wave W_ImageLineProfile KH setscale x, -(lambda*fL)*256/W, (lambda*fL)*256/W,"m", W_ImageLineProfile H H make/O/N=512 wave1D >H setscale x, -(lambda*fL)*256/W, (lambda*fL)*256/W,"m" wave1D YH wave1D =abs( 2*BessJ(1, 2*pi*a*x/(lambda*fL)) / (2*pi*a*x/(lambda*fL))) // Airy formula Hend H HWindow Graph0() : Graph .H PauseUpdate; Silent 1 // building window... 6H Display /W=(32.25,86,470.25,494.75) yTrace vs xTrace H AppendImage wave0_FFT 2H ModifyImage wave0_FFT ctab= {*,*,YellowHot256,0} H ModifyGraph height={Aspect,1} H ModifyGraph lStyle=2 %H ModifyGraph rgb=(65535,65535,65535) H ModifyGraph mirror=2 HEndMacro H HWindow Graph1() : Graph .H PauseUpdate; Silent 1 // building window... 6H Display /W=(33,527,521.25,833.75) W_ImageLineProfile H AppendToGraph/R wave1D H ModifyGraph lSize=1.5 H ModifyGraph lStyle(wave1D)=7 )H ModifyGraph rgb(wave1D)=(0,15872,65280) )H ModifyGraph tick(left)=2,tick(bottom)=2 H ModifyGraph mirror(bottom)=1 !H ModifyGraph lblMargin(bottom)=4 1H ModifyGraph standoff(left)=0,standoff(bottom)=0 iH Legend/C/N=text0/J/A=MC/X=-31.52/Y=28.36 "\\s(W_ImageLineProfile) 2D profile\r\\s(wave1D) Airy formula" HEndMacro D Z $ R   (  j r  |  > l F"fn0^~88V(0NN~rTopicH SubtopicH  SeeAlsoH TopicBody1$H Steps$H TopicBody1a$H NOTElHm  Command $6HZl~ h picture $ Code_Indented1$$6HZl~ Dh Code1a$6HZl~ Dh Code1$6HZl~ Dh Code_Indented1a$$6HZl~Dh Table2 OperationFlags1al Table3 OperationBody1a OperationSectionH  OperationBody1 OperationFlags1l Stepl- Step_text--  RelatedTopicsZ &TopicBody1+$H #``z+eG``3N``-8``"=``C``cH&``un*``d"PNG  IHDR-ʠPtEXtSoftwareIgor Pro&A.IDATx흻:u-\<>A.X}v@ kbZ+($Wp1 ׌$dw"$Ioϻ; ì2w8;sB^;ɧ=6|m蒗N|5FHefAO?!@ Fng$3nH"郢(}C-g獷m/EeVq^{#w,.RWضR88(e?e.dhۦjQzRΌ0x(KA_T"@ xϙ(&\1?bQn/>4*[:^VN'dZE. 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