
Using the Diffraction OTF vs Spatial Frequency plot
The Diffraction OTF vs Spatial Frequency plot is a plot of contrast versus spatial frequency, for specified fields and waves.
To create the plot window:
- Select from the menu Analysis > OTF > Diffraction > vs Spatial Frequency

The OTF is displayed as a function of the spatial frequency. The two dimensional OTF is calculated via fast fourier transform, and both a tangential and a sagittal section is plotted. The tangential scan is plotted as a solid curve. The sagittal scan is plotted as a dashed curve. The curve color is that of the field (see the Sources window).
The diffraction OTF calculation does not work if vignetting factors are used to distort the pupil.
By the nature of the fast Fourier transform, the number of points per side, N, used to sample the pupil is equal to the number of spatial frequencies at which information is obtained about the OTF. These N spatial frequencies are uniformly distributed from zero to the cut-off frequency (the spatial frequency above which the contrast must be zero by diffraction theory). N is also equal to the number of points on the image screen at which information is obtained about the PSF. Increasing N increases the size of the area over which the PSF is obtained. It does not change the spacing of points on the image screen. To obtain smoother PSF or LSF, use Fourier interpolation (controlled by the interpolation order control).
Options panel
Rays tab
- Field
- Using the Field popup menu, select the field for which you wish to calculate. Select All to calculate for all fields (this can be time-consuming).
- Wave
- Using the Wave popup menu, select the wave for which you wish to calculate. If "Polychromatic" is selected, the calculation will be a weighted sum of the various waves.
- Pupil sampling, number of rays per side
- The pupil is sampled using a rectangular N by N grid of points that contains the pupil (if vignetting factors are zero). N is the "number of rays per side".
- Interpolation order
- To produce a smoother PSF or LSF, you can use this control to increase the order of Fourier interpolation used. The pupil data is Fourier transformed to produce the PSF, and this data is then (Fourier) interpolated to increase the resolution. The interpolation order is the number of doublings of the resolution.
- Plot diffraction limit
- Plot the diffraction limit curve: the OTF of an unaberrated system with a circular pupil.
- Spline smoothing
- If checked, the number of points in the plotted curves will be increased using spline interpolation. This gives nicer looking graphs.
- Plot real and imaginary parts
- In addition to plotting the MTF, which is the absolute value of the complex-valued OTF, also plot the real and imaginary parts of the OTF.
- Maximum spatial frequency
- The maximum spatial frequency displayed on the plot. Note that the diffraction calculation generates data from zero frequency to the cut-off frequency, so the number of points plotted will be approximately the number of rays per side multiplied by the ratio of the maximum plotted frequency to the physical cut-off frequency.
- Plot physical range
- Sets the cutoff to plot the entire range of spatial frequencies transmitted by the lens. The maximum spatial frequency is the reciprocal of the product of the wavelength and the working focal ratio.
Tests tab
- Zero all OPD data
- As a check of the DFT calculation, you can use this to clear the OPD, so that a perfect imaging system should be represented.
- Show convolution calculation
- As a check of the DFT calculation, you can use this to perform a brute force calculation of the OTF. The results are plotted as symbols.
- Infinite loop
- For timing purposes, repeats the calculation indefinitely.
- Correct for angle of incidence
- Corrects the spatial frequency for angle of incidence.