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Using the Huygens LSF plot

The Huygens calculator can plot the line-spread function (LSF) or the optical transfer function (OTF), as calculated using the Huygens-Fresnel wavelet theory.

The Huygens calculator window shows a plot of LSF or MTF, and a thumbnail (small image) of the PSF. The thumbnail is useful for troubleshooting.

huygens

To create the LSF plot window:

  1. Select from the menu Analysis > LSF > Huygens

The LSF is displayed as a function of the displacement on the image plane. If the image surface is curved, the plane used is one tangent to the surface at the point where the ray closest to the spot centroid hits the surface. The two directions used are coordinates x and y measured on a plane tangent to the image plane at the centroid of the image spot. The solid curve is the LSF for an object line parallel to the y axis and the displacement axis is x. The dashed curve is the LSF for an object line parallel to the x axis and the displacement axis is y.

The Huygens PSF calculation requires time proportional to the product of the number of arrays and the square of the number of points per side. It becomes very slow if you use many rays, or ask for high resolution. Consider using the spline smoothing option to make the curves smooth.

To allow termination of a time-consuming calculation, you can simply reduce the number of points per side. Whenever you change a parameter the calculator terminates any calculation in progress and restarts with the new parameter.

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 very time-consuming).
Wave
Using the Wave popup menu, select the wave for which you wish to calculate. At present only the monochromatic diffraction OTF may be calculated.
Pattern
For the Huygens calculator, the pattern of rays used to sample the pupil may be specified indpendently of the grid used to sample the image plane. Using the Pattern popup menu, select the pupil pattern to use. If the Random pattern is selected, a randomize (Roll) button will appear and the toolbar Randomize icon will be enabled.
Number of points per side
The image plane is sampled using a rectangular N by N grid of points. N is the "number of points per side". The points are spaced by "delta" which is the next parameter. If you plot the OTF, the number of spatial frequencies at which the OTF is calculated is N/2 (i.e., up to the Nyquist frequency). These N spatial frequencies are uniformly distributed from zero to the physical limit (the spatial frequency at which the contrast must becomes zero by diffraction theory).
Image plane sampling delta
The spacing of the points on the image plane sampling grid. If you change this quantity the width will be recalculated.
Image plane sampling width
The width of the sampling grid, equal to the product of image delta and the number of points per side, N. If you change this quantity delta will be recalculated.

Plot tab

Plot LSF
If checked, the LSF is plotted. If unchecked the OTF is plotted.
Units
Allows selection from a list of length units.
Plot OTF
If checked, the OTF is plotted. If unchecked the LSF is plotted.
Plot diffraction limit
Plot the diffraction limit curve: the LSF or OTF of an unaberrated system with a circular pupil. n.b., assumes Fraunhofer diffraction.
Plot real and imaginary parts
If checked, the real and imaginary parts of the OTF are plotted, as well as its magnitude (MTF).
Maximum spatial frequency
The maximum spatial frequency displayed on the plot. Note that the Huygens calculation allows calculation at spatial frequencies beyond the physical range.
Plot physical range
Sets the maximum spatial frequency to the physical limit: the spatial frequency that is the reciprocal of the product of the wavelength and the working focal ratio.
Divide by focal length
Divide the image space spatial frequency (cycles per unit length) by the focal length of the lens, so that it becomes an angular frequency (cycles per unit angle).
Spline smoothing
Interpolates in the calculated data using a spline, to give a smoother looking curve.

PSF tab

Draw Airy disk
If checked, the Airy disk is drawn. n.b., this enables image resampling.
Draw rays
If checked, the geometrical rays are superimposed on the PSF image. n.b., this enables image resampling.
Resample image
Resamples image to center the pattern and make the image a specified minimum resolution, in case you wish to copy it out or save it.
False-color image
Colors instead of intensity shading.
Enhance faint features
Uses a nonlinear intensity map to amplify weak features.
Negative image
Reverse shading for high and low intensity.

See also