Aberrations (optimization operands by category)

Angular aberration radial direction measured in image space with respect to the centroid at the wavelength defined by Wave. This quantity is defined as:

where l and m are the x and y direction cosines of the ray and the c subscript indicates the centroid. See "Hx, Hy, Px, and Py".

Angular aberration radius measured in image space at the wavelength defined by Wave with respect to the primary wavelength chief ray. This quantity is defined as:

where l and m are the x and y direction cosines of the ray and the c subscript indicates the chief ray. See "Hx, Hy, Px, and Py".

Angular aberration x direction measured in image space at the wavelength defined by Wave with respect to the primary wavelength chief ray. This quantity is defined as:

where l is the x direction cosine of the ray and the c subscript indicates the chief ray. See "Hx, Hy, Px, and Py".

Angular aberration y direction measured in image space at the wavelength defined by Wave with respect to the primary wavelength chief ray. This quantity is defined as:

where m is the y direction cosine of the ray and the c subscript indicates the chief ray. See "Hx, Hy, Px, and Py".

Angular aberration x direction measured in image space at the wavelength defined by Wave with respect to the centroid. This quantity is defined as:

where l is the x direction cosine of the ray and the c subscript indicates the centroid. ANCX has the same restrictions that TRAC does; see TRAC for a detailed discussion. See "Hx, Hy, Px, and Py".

Angular aberration y direction measured in image space at the wavelength defined by Wave with respect to the centroid. This quantity is defined as:

where m is the y direction cosine of the ray and the c subscript indicates the centroid. ANCY has the same restrictions that TRAC does; see TRAC for a detailed discussion. See "Hx, Hy, Px, and Py".

Axial color, measured in lens units for focal systems and diopters for afocal systems. This is the image separation between the two wavelengths defined by Wave1 and Wave2. If Zone is zero, paraxial rays are used to determine the paraxial image locations. If Zone is greater than 0.0 and less than or equal to 1.0, real marginal rays are used to determine the image locations. In this case, Zonecorresponds to the Py coordinate of the real marginal ray.

See "Hx, Hy, Px, and Py".

Biocular Convergence. Returns the convergence between two eye configurations in milliradians. The left and right eye configurations are specified using the Left and Right values. The other parameters are:

Wave: The wavelength number to use.

UseCos: If 0 field units are degrees, otherwise field is in direction cosine units.

Xang/Yang: The X and Y angle or cosines at which to compute the convergence.

If the chief rays from both configurations at the specified angles do not pass through to the image without vignetting, an error is reported. See "Divergence/Convergence" for more information and important assumptions.

Distortion maximum. This specifies an upper bound for the absolute value of the distortion. DIMX is based on the same calculation as DISG, and is not related to the Seidel-based calculations given by DIST. Field can be zero, which specifies that the maximum field coordinate be used, or any valid field number. Note the maximum distortion does not always occur at the maximum field coordinate. DIMX only traces chief rays (Px = Py = 0), and thus Px and Py are not user-defined. The reference field is always an on-axis field point (Hx = Hy = 0), even if such a field point has not been defined in the optical system. See DISG for more information.

The distortion is calculated at the wavelength defined by Wave.

If Absolute is 0, the value returned is in units of percentage. If Absolute is 1, the distortion is given as an absolute length rather than a percentage.

This operand may not be valid for non-rotationally symmetric systems.

Distortion, calibrated. This operand computes the calibrated f-theta distortion across the y-field of view at the wavelength defined by Wave, and returns the absolute value of the maximum deviation from linearity of the f-theta condition.

If Absolute is 0, the value returned is in units of percentage. If Absolute is 1, the distortion is given as an absolute length (for focal systems) or an absolute deviation in cosine space (for afocal systems) rather than a percentage. This operand is useful for designing f-theta lenses.

Generalized distortion, either in percent or as an absolute distance. This operand computes the distortion for any ray in the pupil, from anywhere in the field, at the wavelength defined by Wave, using the field point defined by Field as a reference. The method used and assumptions made for DISG calculations are common to all operands that calculate distortion. DISG cannot be calculated if the field units are angles and the maximum angle equals or exceeds 90 degrees. DISG assumes the predicted magnification is not symmetric.

If the field is defined in terms of angles, the normalized field coordinates Hx and Hy are defined as:

H=θ/θ_M

where θ is the absolute angle measured from the central on-axis field, and θ_M is the maximum field angle (see "Maximum field").

If Waveis a positive number, DISG returns the distortion as a percentage. If Wave is a negative number, the absolute value of Wave is used to define the wavelength and the returned value is in units of absolute length rather than percentage.

As with all distortion concepts, the best way to avoid confusion and misleading results is to use finite object distances and object heights to define fields rather than field angles.

See "Hx, Hy, Px, and Py".

Distortion in waves contributed by the surface defined by Surf at the wavelength defined by Wave. This is the third order distortion calculated from the Seidel coefficients (see "Seidel Coefficients"), and is not valid for non-paraxial systems.

If Surf is zero, the distortion is given in percent instead (see "Field Curvature/Distortion" for a detailed definition).

If Absolute is set to 1, and the surface number is zero, the distortion is given as an absolute length rather than a percentage.

See also DISG.

Generalized field curvature, sagittal. The field curvature value for any field point, at the wavelength defined by Wave. The value is generalized to return reasonable results even for non-rotationally symmetric systems; see "Field Curvature/Distortion".

See "Hx, Hy, Px, and Py".

Longitudinal aberration, measured in lens units for focal systems and diopters for afocal systems. This is the defocus from the current image to the image at the wavelength defined by Wave and pupil zone defined by Zone. If Zone is zero, paraxial rays are used to determine the paraxial image locations. If Zone is greater than 0.0 and less than or equal to 1.0, real marginal rays are used to determine the image locations. In this case, Zone corresponds to the Py coordinate of the real marginal ray.

See AXCL.

Optical path difference with respect to the mean OPD over the pupil with tilt removed at the wavelength defined by Wave. OPDX has the same restrictions that TRAC does; see TRAC for a detailed discussion.

See "Hx, Hy, Px, and Py".

RMS wavefront error with respect to the centroid in waves. This operand uses a Gaussian quadrature method that is accurate for systems with unvignetted circular pupils. Ring is used to specify the number of rings of rays traced. If Wave is zero; then a wavelength weighted polychromatic calculation is performed; otherwise, the specified wavelength number will be used.

See "Hx, Hy, Px, and Py", and "OPTIMIZATION REFERENCE POINTS".

RMS wavefront error with respect to the chief ray in waves. This operand uses a Gaussian quadrature method that is accurate for systems with unvignetted circular pupils. Ring is used to specify the number of rings of rays traced. If Wave is zero; then a wavelength weighted polychromatic calculation is performed; otherwise, the specified wavelength number will be used.

See "Hx, Hy, Px, and Py" , and "OPTIMIZATION REFERENCE POINTS".

RMS wavefront error with respect to the centroid in waves. This operand uses a rectangular grid of rays to estimate the RMS. This operand considers vignetting. A Samp value of n will trace an n x n grid per pupil quadrant. If Wave is zero; then a wavelength weighted polychromatic calculation is performed; otherwise, the specified wavelength number will be used.

See "Hx, Hy, Px, and Py", and "OPTIMIZATION REFERENCE POINTS".

RMS wavefront error with respect to the chief ray in waves. This operand uses a rectangular grid of rays to estimate the RMS. This operand considers vignetting. A Samp value of n will trace an n x n grid per pupil quadrant. If Wave is zero; then a wavelength weighted polychromatic calculation is performed; otherwise, the specified wavelength number will be used.

See "Hx, Hy, Px, and Py", and "OPTIMIZATION REFERENCE POINTS".

Spherochromatism in lens units. This is the difference between the real marginal axial color and the paraxial axial color of the two extreme wavelengths defined by Minw and Maxw. The distance is measured along the Z axis. Zone defines the zone for which the real marginal axial color is computed. Zone corresponds to the Py coordinate of the real marginal ray.

Not valid for non-paraxial systems.

Transverse aberration radial direction measured in image space with respect to the centroid for the wavelength defined by Wave. Unlike most other operands, TRAC critically depends upon the placement of other TRAC operands within the Merit Function Editor to work correctly. TRAC operands must be grouped together by field position and wavelength. OpticStudio traces all TRAC rays with a common field point together, and then uses the collective data to compute the centroid of all the rays. Each ray individually is then referenced to the computed centroid. This operand should only be entered into the Merit Function Editor by the Sequential Merit Function tool, and is not recommended for use directly by the user.

See "Hx, Hy, Px, and Py".

Transverse aberration radius measured at the surface defined by Surf at the wavelength defined by Wave with respect to the chief ray. Similar to TRAR, except a surface other than the image surface may be specified.

See "Hx, Hy, Px, and Py".

Transverse aberration radial direction measured in image space at the wavelength defined by Wave with respect to the chief ray. See ANAR.

See "Hx, Hy, Px, and Py".

Transverse aberration x direction measured in image space at the wavelength defined by Wave with respect to the chief ray.

See "Hx, Hy, Px, and Py".

Transverse aberration y direction measured in image space at the wavelength defined by Wave with respect to the chief ray.

See "Hx, Hy, Px, and Py".

Zernike Fringe coefficient. The parameters are:Term: The Zernike term number (1 - 37 for fringe, 1 - 231 for standard or annular).The Term value, if negative or zero, may also be used to return other data from the Zernike fitting as follows:

-8: Peak to Valley OPD (to centroid)-7: Peak to Valley OPD (to chief)-6: RMS to zero reference (unused by OpticStudio)-5: RMS to chief ray-4: RMS to centroid-3: Variance-2: Strehl Ratio-1: RMS fit error0: Maximum single point fit error

Wave: The wavelength number.Samp: The pupil sampling, where 1 yields 32 x 32, 2 yields 64 x 64 etc.Field: The field number.Type: The Zernike type (0 for fringe, 1 for standard, 2 for annular).Epsilon: The obscuration ratio (for annular coefficients only).Vertex?: If 1, the OPD is referenced to the surface vertex. If 0, the OPD is referenced to the chief ray.

Note that if you use multiple ZERN operands which only differ in the Term value, they should be placed on adjacent lines in the editor so OpticStudio only does the fitting once; otherwise, the computation is slower. Multiple Zernike terms are always used in the fitting process, even if only one coefficient is requested. The maximum number of terms used in the computation depends on the Type and the Term settings. The minimum number of terms used for all types is 11. This means that Term is only used if set greater than or equal to 11. If Type is standard or annular, the maximum term number computed is set equal to the largest term requested by any Term value in adjacent ZERN operands.

Note that a "ZERN error" message may occasionally appear, usually caused by insufficient RAM or if OpticStudio is unable to compute the OPD. There are a number of other situations that can trigger this error message. If you suspect none of the above reasons apply to your case, please contact technical support.