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RMS spot size meritoid

This meritoid is normally used with a target of zero.

The calculation has two modes, depending on the target value:

Multi-residual mode (target equal to zero)
The ray deviations for the traced rays, divided by the tolerance, are passed independently to the optimizer as residuals. This allows the Levenberg-Marquardt method to "see" the spot diagram and zero-in efficiently on the minimum spot size.
Mono-residual mode (target not equal to zero)
The ray deviations for the traced rays are collapsed to a single number: the RMS spot size. The deviation of this single number from the specified target value, divided by the tolerance, is passed to the optimizer as a residual. In this case the Levenberg-Marquardt method can have difficulties if the RMS spot size can not be made to cross the target (this method assumes that residuals do not have turning points near the minimum of the merit function).

Parameters

Analysis direction

x
The display value is the RMS width of the x-profile. The multi-residual is the set of x deviations, divided by the tolerance. The number of residuals is equal to the number of rays.
y
The display value is the RMS width of the y-profile. The multi-residual is the set of y deviations, divided by the tolerance. The number of residuals is equal to the number of rays.
r
The display value is the RMS spot size in the xy-plane. The multi-residual is the union of the set of x deviations and the set of y deviations, divided by the tolerance. The number of residuals is twice the number of rays.

Field coordinate

Hx and Hy are the reduced field coordinates (between -1 and 1) of the image point for which the calculation is to be performed.

Polychromatic/Monochromatic

Selecting Polychromatic will use the specified wavelengths and weights from the Sources window. Selecting Monochromatic will use the wavelength specified in the combo box (you can use the arrow to pick from any of the defined wavelengths or you can enter your own value. The wavelength is specified in nanometers (nm).

# of rays

The rays traced fill the pupil on a hexapolar pattern assuming a circular pupil, with the ring spacing such that the pupil radius is half-way between rings. The number of points will automatically adjust itself to a hex number (1, 7, 19, 37, 61, 91, ...).

Units

The units pop-up menu allows you to select what units of length are to be used to display the result and to calculate the residual.

units popup menu

Selecting "waves" from the units menu causes the result to be expressed in terms of the wavelength of the primary wave.

Target

The target is specified in the same units as the displayed value. If the target is zero (the usual case) the meritoid is multi-residual, as described above. If the target is non-zero the meritoid returns a single number for the residual.

Tolerance

The tolerance is specified in the same units as the displayed value and specified target. Using this tolerance a dimensionless residual is created in the usual way.

See also