Optimization Operands (Alphabetically)

Cardinal Point data. This operand will return the location of the 6 cardinal points for object space and 6 cardinal points for image space, including principal, anti-principal, nodal, anti-nodal and focal planes, in Lens units. The calculation is performed for any defined wavelength and either the X-Z or Y-Z plane orientations. Object space positions are measured with respect to the surface defined as Surf1, and the image space positions are measured with respect to the surface defined as Surf2. The index in both the object space and image space is considered.

Surf1: The starting surface number of the group to compute the cardinal points for.

Surf2: The ending surface number of the group to compute the cardinal points for.

Wave: The wavelength number to use for the computation.

Orientation: The orientation to use for computing the cardinal plane locations (0 – YZ plane or 1 – XZ plane).

The value returned depends upon the value of Data as follows:

0 – Object Space Focal Length

1 – Image Space Focal Length

2 – Object Space Focal Plane

3 – Image Space Focal Plane

4 – Object Space Principal Plane

5 – Image Space Principal Plane

6 – Object Space Anti-Principal Plane

7 – Image Space Anti-Principal Plane

8 – Object Space Nodal Plane

9 – Image Space Nodal Plane

10 – Object Space Anti-Nodal Plane

11 – Image Space Anti-Nodal Plane

The curvature data in lens units of the surface defined by Surf. Curvature data includes the Mean, PV, Minimum, or Maximum curvature value across a specified surface as well as the X or Y coordinates of Min curvature value, or the X or Y coordinates of the Max curvature value. This operand has data, sampling, off-axis, remove, best-fit sphere (BFS), and Orientation flags.

The options for the Data input will be:

1 – RMS curvature value over the surface.

2 – PV curvature value over the surface.

3 – Minimum curvature value over the surface.

4 – Maximum curvature value over the surface.

5 – X coordinate for the point on the surface with the minimum curvature value.

6 – Y coordinate for the point on the surface with the minimum curvature value.

7 – X coordinate for the point on the surface with the maximum curvature value.

8 – Y coordinate for the point on the surface with the maximum curvature value.

9 – ROC of the best-fit sphere

10 – Z Offset of the best-fit sphere vertex from the local coordinate system

11 – X decenter of off-axis coordinate system from the surface's local coordinate system

12 – Y decenter of off-axis coordinate system from the surface's local coordinate system

13 – Z decenter of off-axis coordinate system from the surface's local coordinate system

14 – Tilt about X (a) of off-axis coordinate system, from the surface's local coordinate system

15 – Tilt about Y (b) of off-axis coordinate system, from the surface's local coordinate system

16 – Tilt about Z (g) of off-axis coordinate system, from the surface's local coordinate system

The options for the Samp input will be:

1 – 33 x 33 (default)

2 – 65 x 65

3 – 129 x 129

4 – 257 x 257

5 – 513 x 513

6 – 1025 x 1025

7 – 2049 x 2049

8 – 4097 x 4097

9 – 8193 x 8193

10 – 16385 x 16385

• Off-axis = 0 (default) the computation is calculated with respect to the system coordinates and Off-axis = 1 the computation is calculated with respect to a tilted and decentered coordinate system, where the origin of the coordinate system falls at the vertex of the off-axis part. The X and Y inputs will then refer to coordinates in the new off-axis coordinate system.
• Remove = 0 (default) no data is removed. Remove = 1 the base radius of curvature is removed from the data before calculation. Remove = 2 the best-fit sphere is removed from the data before calculation.
• BFS selects which type of best-fit sphere to remove from the data if Remove is set to 2. BFS = 0 (default) for minimum volume best-fit sphere. BFS = 1 for Minimum RMS best-fit sphere. BFS = 2 for Minimum RMS best-fit sphere with offset. The offset allows the calculation to shift the vertex of the BFS away from the data value at the vertex if it results in a lower RMS.
• Orientation selects the direction of the curvature calculation. Orientation = 0 (default) calculated along the tangential direction. Orientation = 1 calculated along the sagittal direction. Orientation = 2 calculated along the X-axis direction. Orientation = 3 calculated along the Y-axis direction. Orientation = 4 is the modulus or length of the curvature vector, at the orientation angle that contains the full length of the vector (The angle is not explicitly calculated and can vary between points on the curvature map).

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.

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 Wave is 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".

The phase data in waves at the primary system wavelength of the surface defined by Surf. Phase data includes the RMS, PV, Minimum, or Maximum phase value across a specified surface as well as the X or Y coordinates of Min phase value, or the X or Y coordinates of the Max phase value. This operand has data, sampling, and remove flags.

The options for the Data input will be:

1 – RMS phase value over the surface.

2 – PV phase value over the surface.

3 – Minimum phase value over the surface.

4 – Maximum phase value over the surface.

5 – X coordinate for the point on the surface with the minimum phase value.

6 – Y coordinate for the point on the surface with the minimum phase value.

7 – X coordinate for the point on the surface with the maximum phase value.

8 – Y coordinate for the point on the surface with the maximum phase value.

9 – Value of the constant phase removed from the data.

10 – Value of the tilt about X removed from the data.

11 – Value of the tilt about Y removed from the data.

12 – Value of the power removed from the data.

The options for the Samp input will be:

1 – 33 x 33 (default)

2 – 65 x 65

3 – 129 x 129

4 – 257 x 257

5 – 513 x 513

6 – 1025 x 1025

7 – 2049 x 2049

8 – 4097 x 4097

9 – 8193 x 8193

10 – 16385 x 16385

• Remove = 0 (default) no data is removed. Remove = 1 constant value at the vertex of the part is removed from the data . Remove = 2 the tilt term is removed from the data. Remove = 3 the power term is removed from the data.

The sag data in lens units of the surface defined by Surf. Sag data includes the RMS, PV, Minimum, or Maximum sag value across the specified surface as well as the X or Y coordinates of Min sag value, or the X or Y coordinates of the Max sag value. This operand has data, sampling, off-axis, remove, and best-fit sphere (BFS) flags.

The options for the Data input will be:

1 – RMS sag value over the surface (default).

2 – PV sag value over the surface.

3 – Minimum sag value over the surface.

4 – Maximum sag value over the surface.

5 – X coordinate for the point on the surface with the minimum sag value.

6 – Y coordinate for the point on the surface with the minimum sag value.

7 – X coordinate for the point on the surface with the maximum sag value.

8 – Y coordinate for the point on the surface with the maximum sag value.

9 – Radius of curvature of the best-fit sphere.

10 – Z Offset of the best-fit sphere vertex from the local coordinate system.

11 – X decenter of off-axis coordinate system from the surface's local coordinate system.

12 – Y decenter of off-axis coordinate system from the surface's local coordinate system.

13 – Z decenter of off-axis coordinate system from the surface's local coordinate system.

14 – Tilt about X (a) of off-axis coordinate system, from the surface's local coordinate system.

15 – Tilt about Y (b) of off-axis coordinate system, from the surface's local coordinate system.

16 – Tilt about Z (g) of off-axis coordinate system, from the surface's local coordinate system.

The options for the Samp input will be:

1 – 33 x 33 (default)

2 – 65 x 65

3 – 129 x 129

4 – 257 x 257

5 – 513 x 513

6 – 1025 x 1025

7 – 2049 x 2049

8 – 4097 x 4097

9 – 8193 x 8193

10 – 16385 x 16385

• Off-axis = 0 (default) the computation is calculated with respect to the system coordinates and Off-axis = 1 the computation is calculated with respect to a tilted and decentered coordinate system, where the origin of the coordinate system falls at the vertex of the off-axis part. The X and Y inputs will then refer to coordinates in the new off-axis coordinate system.
• Remove = 0 (default) no data is removed. Remove = 1 the base radius of curvature is removed from the data before calculation. Remove = 2 the best-fit sphere is removed from the data before calculation.
• BFS selects which type of best-fit sphere to remove from the data if Remove is set to 2. BFS = 0 (default) for minimum volume best-fit sphere. BFS = 1 for Minimum RMS best-fit sphere. BFS = 2 for Minimum RMS best-fit sphere with offset. The offset allows the calculation to shift the vertex of the BFS away from the data value at the vertex if it results in a lower RMS.

The slope data in lens units of the surface defined by Surf. Slope data includes the Mean, PV, Minimum, or Maximum slope value across a specified surface as well as the X or Y coordinates of Min slope value, or the X or Y coordinates of the Max slope value. This operand has data, sampling, off-axis, remove, best-fit sphere (BFS), and Orientation flags.

The options for the Data input will be:

1 – RMS slope value over the surface (default).

2 – PV slope value over the surface.

3 – Minimum slope value over the surface.

4 – Maximum slope value over the surface.

5 – X coordinate for the point on the surface with the minimum slope value.

6 – Y coordinate for the point on the surface with the minimum slope value.

7 – X coordinate for the point on the surface with the maximum slope value.

8 – Y coordinate for the point on the surface with the maximum slope value.

9 – ROC of the best-fit sphere.

10 – Z Offset of the best-fit sphere vertex from the local coordinate system.

11 – X decenter of off-axis coordinate system from the surface's local coordinate system.

12 – Y decenter of off-axis coordinate system from the surface's local coordinate system.

13 – Z decenter of off-axis coordinate system from the surface's local coordinate system.

14 – Tilt about X (a) of off-axis coordinate system, from the surface's local coordinate system.

15 – Tilt about Y (b) of off-axis coordinate system, from the surface's local coordinate system.

16 – Tilt about Z (g) of off-axis coordinate system, from the surface's local coordinate system.

The options for the Samp input will be:

1 – 33 x 33 (default)

2 – 65 x 65

3 – 129 x 129

4 – 257 x 257

5 – 513 x 513

6 – 1025 x 1025

7 – 2049 x 2049

8 – 4097 x 4097

9 – 8193 x 8193

10 – 16385 x 16385

• Off-axis = 0 (default) the computation is calculated with respect to the system coordinates and Off-axis = 1 the computation is calculated with respect to a tilted and decentered coordinate system, where the origin of the coordinate system falls at the vertex of the off-axis part. The X and Y inputs will then refer to coordinates in the new off-axis coordinate system.
• Remove = 0 (default) no data is removed. Remove = 1 the base radius of curvature is removed from the data before calculation. Remove = 2 the best-fit sphere is removed from the data before calculation.
• BFS selects which type of best-fit sphere to remove from the data if Remove is set to 2. BFS = 0 (default) for minimum volume best-fit sphere. BFS = 1 for Minimum RMS best-fit sphere. BFS = 2 for Minimum RMS best-fit sphere with offset. The offset allows the calculation to shift the vertex of the BFS away from the data value at the vertex if it results in a lower RMS.
• Orientation selects the direction of the slope calculation. Orientation = 0 (default) calculated along the tangential direction. Orientation = 1 calculated along the sagittal direction. Orientation = 2 calculated along the X-axis direction. Orientation = 3 calculated along the Y-axis direction. Orientation = 4 is the modulus, or length of the slope vector.

Fiber coupling efficiency for single mode fibers. The calculated value is the total coupled energy efficiency, relative to unity. The parameters of this operand are:

Samp: The pupil sampling, where 1 yields 32 x 32, 2 yields 64 x 64 etc.

Wave: The wavelength number to use.

Field: The integer field position number.

IgSrc: If this parameter is zero, then the object source fiber is considered; otherwise, the object source fiber is ignored.

Sna: The source fiber NA.

Rna: The receiver fiber NA.

Pol?: Set to 0 to ignore polarization and 1 to consider it.

See "Fiber Coupling Efficiency" for details. See also FICP.

Fiber coupling as computed using the Physical Optics Propagation (POP) algorithm, using whatever the current default settings are for the POP feature.

Surf: This controls the end surface used in the POP calculation.  If Surf is zero, then the saved ending surface number will be used; otherwise, the specified surface will be used as the ending surface.

Wave: This controls the wavelength used in the POP calculation.  If Wave is zero, then the saved wavelength number will be used; otherwise, the specified wavelength number will be used.

Data: This controls what data is returned. If Data is 0 the total power coupling is returned. If Data is 1, the amplitude coupling for the Ex field is returned. If Data is 2 or 3, the real or imaginary part of the amplitude coupling for the Ex field is returned, respectively. If Data is 4, the amplitude coupling for the Ey field is returned. If Data is 5 or 6, the real or imaginary part of the amplitude coupling for the Ey field is returned, respectively. If the beam is unpolarized the Ey values wil be zero.

Data inputs 1-6 request a polarized POP calculation, but if the input beam is unpolarized, the field coupling efficiency amplitudes and phases are not physically well-defined. Therefore, values of 0.0 will be returned if the input beam is unpolarized.

To use this operand, first define the settings on the POP analysis feature as desired, then press Save on the settings box. The operand FICP will return the same efficiency as computed by the POP feature.

Field: This controls the field number used in the POP calculation. If Field is zero, then the saved field number will be used; otherwise, the specified field number will be used.

This operand is redundant with the more general POPD.

See " Computing Fiber Coupling ". See also FICL.

Ghost angle of incidence. This operand calculates the angle of incidence of a ray in degrees at any surface after a double-bounce ghost reflection.

The Surf1 and Surf2 values define the first and second surface numbers to define the ghost path. Note the first bounce surface number must be larger than the second bounce surface number. The primary wavelength is always used. Surf3 determines the surface at which the angle of incidence is computed and has to be greater than Surf2. When Surf3 is negative, its absolute value directly specifies the surface number in the ghost system. See "Ghost Focus Generator" for more information of ghost systems. By default, the SetVig = 0. When SetVig = 1, vignetting factors are set for the ghost system when calculating the angle of incidence. Note that setting vignetting factors will cause beams to fully pass all surface apertures when possible by shifting and shrinking the beams. See "Vignetting."

Note that if Surf2 is a mirror in the original system, the beam cannot reach the image surface in ghost system. Therefore Surf3 can only be 0 or negative. Surf3 = 0 represents the last surface in the ghost system, which is the object surface in the original system.

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

TrueFreeForm surface constraints. This operand computes various values from the shape of a TrueFreeForm surface. Surf is the surface number. The Data value determines what value is computed by the operand as follows:

1: Minimum Z value.

2: Maximum Z value.

3: Minimum Z increment. This is the smallest difference between adjacent Z control points.

4: Maximum Z increment. This is the biggest difference between adjacent Z control points.

Once the Data has been computed, the Mode value determines how the operand behaves. The Mode parameter works as follows:

1: Returns the data.

2: Returns the data value only if the data value is less than the target value, otherwise the target value is returned. This mode is used to enforce a "greater than" boundary on the data.

3: Returns the data value only if the data value is greater than the target value, otherwise the target value is returned. This mode is used to enforce a "less than" boundary on the data.

Test for the hyperhemisphere condition. OpticStudio traces the specified ray at the wavelength defined by Wave to the surface defined by Surf, and computes the x, y, and z intercept coordinates. Then, the x and y coordinates only are used in the sag expression for that surface to see what z coordinate results. If the z coordinates are not the same, then HHCN returns 1, otherwise it returns zero. This operand can be used to prevent optimizations from reaching solutions that require hyperhemispheric surface shapes.

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

Moore-Elliott Contrast, average of sagittal and tangential. This operand uses the Moore-Elliott Contrast method to optimize the MTF at a given spatial frequency. See " Optimizing for MTF " for more information on the Moore-Elliott Contrast method. The parameters are:

Wave The wavelength number to use.

Field The field number.

Freq The spatial frequency in cycles per millimeter in focal systems and cycles per afocal unit (see "Afocal Mode Units") in afocal systems.

See "Hx, Hy, Px, and Py". Also see related operands MECS and MECT.

Minimum angle of incidence. This boundary operand traces the marginal and chief rays from defined Field and reports the minimum angle at the surface defined by Surf.

Surf: The surface number to use. Use Surf = 0 for all surfaces (default).

Wave: The wavelength number to use. Use Wave = 0 for all wavelengths (default).

Field: The integer field number to use. Use Field = 0 for all fields (default).

Symmetry: Define if X or Y symmetry exists to only trace marginal rays along one axis. Use Symmetry = 0 to trace all the marginal and gut rays (default). Use Symmetry = 1 for y-symmetric systems (only traces gut and y-marginal rays) and Symmetry = 2 for x-symmetric systems.

Data: Define what value is computed.

0: Minimum angle (default).

1: Ray number (0 = gut, 1 = +y, 2 = -y, 3 = +x, 4 = -x)

2: Field number of minimum angle ray

3: Wavelength number of minimum angle ray

4: Surface number of minimum angle ray

Wave: The wavelength number to use (use 0 for polychromatic).

Field: The field number. To extract the diffraction-limited MTF use field equal 0 and Grid parameter equal 1. Similar options available for for the MTFS, MTFT, MTFN, and MTFX operands.

Freq: The spatial frequency in MTF units (see "MTF Units"). If the sampling is set too low for accurate computation of the MTF, then the MTF operands all return zero. If both the tangential and sagittal MTF are needed; place the MTFT and MTFS operands on adjacent lines and they will be computed simultaneously. See "Performing an optimization".

Data Type: Specifies the data to be returned. An input of 0 will return the modulation amplitude; an input of 1 will return the real part; an input of 2 will return the imaginary part; an input of 3 will return the phase. This input is only available for the MTFA, MTFS, and MTFT operands (and not the equivalent square-wave operands).

Non-sequential PAF file. "PAF File" defines the name of the PAF file to be saved (up to 140 characters).

This operand must come before the NSTR operand in the Merit Function.

NPXG

Non-sequential object position x greater than. Surf defines the surface number of the NSC group (always 1 in pure NSC systems). Object defines the object number in the NSC group.

If Ref? is 0, the coordinates are relative to the reference object.

If Ref? is 1, the coordinates are relative to the origin of the NSC coordinate system or entry port. If Ref? is 2, then the coordinates are relative to the global coordinate reference surface.

Non-sequential incoherent intensity data. Surf defines the surface number of the NSC group (always 1 in pure NSC systems). Det# refers to the object number of the desired detector. If Det# is zero, then all detectors are cleared. If Det# is less than zero, then the detector defined by the absolute value of Det# only is cleared. Note that one NSDD operand clearing all detectors must be present prior to any subsequently defined NSDD operands.

For Detector Rectangles, Detector Surfaces, and all faceted detectors: If Pix# is a positive integer greater than zero, then the data from the specified pixel is returned. Otherwise, the following data is returned depending upon the value of Pix#:

0: Total flux in position space for all pixels when Data = 0. Average flux/area in position space when Data = 1. Total flux in angle space for all pixels when Data = 2. Note, by default, the angle space of Detector Rectangle is fully defined by -90 ~ 90 degrees in both X and Y directions, and thus the value of Data = 0 and 2 will be same.

-1: Maximum flux, flux/area, or flux/solid angle.

-2: Minimum flux, flux/area, or flux/solid angle.

-3: Number of total rays striking the detector for all pixels. Data is no used when Pix# is set to this value.

-4: Standard deviation (RMS from the mean) of all the non-zero pixel data.

-5: The mean value of all the non-zero pixel data.

-6, -7, -8: The x, y, or z coordinate of the position or angle Irradiance or Intensity centroid, respectively. Note for Detector Rectangle, the value for Data = 0 and 1 will be same because all pixels have same size.

-9,-10, -11, -12, -13: The weighted RMS radius, x, y, z, or xy cross term distance or angle of all the pixel data with respect to the centroid. These are the square root of the variance or second moments r^2, x^2, y^2, z^2, and xy, respectively.

The weighted RMS x is the square root of the variance x^2.

The variance x^2 is equal to:

where w_i is a weight equal to the value of the pixel based on Data, x_i is the x-coordinate of the pixel and x* is the weighted mean.

Note for Detector Rectangle, the value for Data = 0 and 1 will be same because all pixels have same size. Calculations for y* are analogous to those for x*.

-14, -15: The Geometric MTF in X or Y direction. Results will only be available for Data = 0 or Data = 1, and the results will be the same for both Data inputs.

Spatial Frequency is used to specify the spatial frequency (in cycles/millimeter) at which the MTF data is calculated. The Spatial Frequency parameter is only considered when applied to a Detector Rectangle and Pix# is set to -14 or -15.

Data is 0 for flux, 1 for flux/area, 2 for flux/solid angle pixel, 3 for normalized flux, 4 for absorbed flux, and 5 for absorbed flux/area. Note Data = 2 is only available for Detector Rectangle, which records data in angle space. Only values 0 and 1 (for flux and flux/area) are supported for faceted detectors. A value of 3 is only supported when Pix# is a positive integer; in this case the returned flux for the pixel is normalized to the peak flux for all consecutive NSDD operands in the Merit Function Editor which refer to the same surface and detector. A value of 3 should generally be used only as a part of the NSC Bitmap Merit Function (see "NSC Bitmap Merit Function Tool").

For Detector Rectangles only: If Pix# is not a positive integer, then a number of edge pixels may be ignored in the calculation if desired. The number of edge pixels that will be ignored is given by the # Ignored input. For non-zero values of # Ignored, the number of pixels accounted for in the calculation will be reduced along all boundaries of the detector. For example, if a detector has 100 pixels in X and 200 pixels in Y and the # Ignored value is 2, then the calculation will be based upon detector data from 96 pixels in X and 196 pixels in Y, with data from the last 2 edge pixels along the left, right, bottom and top boundaries all ignored. The only calculation not affected by the # Ignored input is the number of rays striking the detector, as given by Pix # = -3 (in addition to all values calculated for positive integer inputs to Pix #).

For Detector Volumes: Pix# is interpreted as the voxel number. For Data values of 0, 1, or 2, the returned value is incident flux, absorbed flux, or absorbed flux per unit volume, respectively. If Pix# is zero, the value returned is the sum for all pixels.

For Object Is A Detector: There are two additional options for data. Data is 4 for absorbed flux and 5 for absorbed flux/area.

For Detector Color objects, use NSDE instead. For Detector Polar objects, use NSDP.

For information about optimization in Non-Sequential Mode, see "NSC Operands"

Non-sequential Detector Color object data. Surf defines the surface number of the NSC group (always 1 in pure NSC systems). Det# refers to the object number of the desired detector. If Det# is zero, then all detectors are cleared. If Det# is less than zero, then the detector defined by the absolute value of Det# only is cleared.

If Pix# is a positive integer greater than zero, then the data from the specified pixel is returned. Otherwise, the following data is returned depending upon the value of Pix#: 0: Sum of all data for all pixels on the detector. For chromaticity coordinates this is the average over all pixels in the detector that have non-zero lumen values. If Pix# is zero the <area> values described below are the area of the entire detector, measured in analysis units for position space data or solid angle in steradians for angle space data.

-1: Maximum data.

-2: Minimum data.

-3: Number of rays striking the detector.

Angle? is 0 for position space data, 1 for angle space data.

Data is an integer code that defines the type of data to return, defined as follows:

1: power in <sprefix> watts where <sprefix> is the source units prefix.

2: power/area in <aprefix> watts per <area> where <aprefix> is the analysis units prefix. If Angle? is 0 <area> is the area in analysis units. If Angle? is 1 then <area> is solid angle in steradians.

3: power in <sprefix> lumens where <sprefix> is the source units prefix.

4: power/area in <aprefix> lumens per <area> where <aprefix> is the analysis units prefix. If Angle?

is 0 <area> is the area in analysis units. If Angle? is 1 then <area> is solid angle in steradians.

5/6: CIE 1931 chromaticity coordinate x/y.

7/8: CIE 1976 chromaticity coordinate u'/v'.

9/10/11: CIE 1931 tristimulus X/Y/Z value in lumens per <area>. If Angle? is 0 <area> is the area in analysis units. If Angle? is 1 then <area> is solid angle in steradians.

12/13: Color Rendering Index (CRI) and Correlated Color Temperature (CCT), the latter value in Kelvin. These values are only returned if the option to "Record Spectral Data" has been selected for the Detector Color object (only available in OpticStudio-Premium) and if the Pix# and Angle? are both zero. The returned values are based on the variation of flux with wavelength over the entire detector.

14/15/16: Normalized CIE 1931 tristimulus X/Y/Z value. Identical to the values returned by Data 9, 10, and 11, but normalized to the peak tristimulus Y value for all consecutive NSDE operands in the Merit Function Editor which refer to the same surface and detector. Generally used only as a part of the NSC Bitmap Merit Function (see "NSC Bitmap Merit Function Tool"). Only valid if Pix# is a positive integer and Angle? is zero.zero.

17/18/19/20/21: The Centroid X, Y and RMS radius, X, Y in Specified Spectral Bin. See description of Wavelength Column for specifying the Spectral Bin. See Detector Settings in Type Section of the Object Properties for defining Spectral Range of Bins.

Wavelength specifies which Spectral Bin's data is calculated for centroid X/Y and RMS radius/X/Y. If the value of Wavelength is inside one Bin's Spectral Range, the Bin's data will be selected for calculation. See "Record Spectral Data" for details of Spectral Binning.

If Pix# is not a positive integer, then a number of edge pixels may be ignored in the calculation if desired. The number of edge pixels that will be ignored is given by the # Ignored input. For non- zero values of # Ignored, the number of pixels accounted for in the calculation will be reduced along all boundaries of the detector. For example, if a detector has 100 pixels in X and 200 pixels in Y and the # Ignored value is 2, then the calculation will be based upon detector data from 96 pixels in X and 196 pixels in Y, with data from the last 2 edge pixels along the left, right, bottom and top boundaries all ignored.

Calculations that are not affected by the # Ignored input are the number of rays striking the detector, as given by Pix # = -3, and the CRI and CCT values, as given by Data = 12 and Data = 13, respectively (the # Ignored input also does not affect any values calculated for positive integer inputs to Pix #). If the source units are joules, then the data 1 and 2 are in joules and data 3 and 4 are in talbots. See " Units ". See also NSDD and NSDP.

Non-sequential single ray trace. Src# refers to the object number of the desired source. This source must be defined to trace just a single analysis ray. If Splt? is non-zero, then splitting is on. If Pol? is non-zero then polarization will be used. If splitting is on polarization is automatically selected.

Scattering is always turned off for this feature, since scattering introduces random paths for the child rays, which is not suitable for optimization. Errors are always considered.

If multiple NSRA operands trace the same ray are adjacent in the merit function editor, the ray will only be traced once for efficiency.

Seg# refers to the segment number that contains the data to be returned. Use -1 for the last segment.

Data refers to the data type for the specified segment.

Use Data values 1-9 for x-coordinate, y-coordinate, z-coordinate, x-cosine, y-cosine, z-cosine, x- normal, y-normal, and z-normal, respectively. These values are relative to the entry port, see 31- 39 below.

Use Data values 10-15 for path-to, intensity, phase of, phase at, index, and starting phase, respectively. Note that the phase at value is not modulo 2*pi, as is the case with ZRD files.

Use Data values 16-17 for the sum of the path, or optical path, respectively, in lens units from the source to the end of the specified segment. These values do not include the phase of diffractive surfaces.

Use Data values 21-26 for Ex real, Ex imaginary, Ey real, Ey imaginary, Ez real, and Ez imaginary, respectively. Polarization must be on for real and imaginary data to be returned.

Use Data value 27-29 for the phase of Ex, Ey, and the phase difference between Ex and Ey, respectively. All values are in radians. Polarization must be on for valid data to be returned.

Use Data values 31-39 for the coordinate data defined by Data values 1-9 converted to coordinates relative to the global coordinate reference surface.

Source # refers to the element number to use if the source is an array; see the "Sources" settings in the Object Properties for the numbering scheme.

Note the segments NSRA is not listed in same order as in ZRD. For example, for a same ray, the segment with Seg# =17 in NSRA is not same to the 17th segment listed in ZRD.

Note the phase_at (Data = 13) is referenced to the center of the pixel where the ray hits on the detector. See more explanations in section "Ray database (ZRD) files".

For more information on these data items see "The ZRD Uncompressed Full Data Format (UFD)".

Physical Optics Propagation Data. For important details see "About Physical Optics Propagation".To use this operand, first define the settings on the POP analysis feature as desired, then press Save on the settings box. The operand will return data based upon the selected settings.

If Surf is zero, then the saved ending surface number will be used; otherwise, the specified surface will be used as the ending surface. If Wave is zero, then the saved wavelength number will be used; otherwise, the specified wavelength number will be used. If Field is zero, then the saved field number will be used; otherwise, the specified field number will be used.

Data determines what data the POP feature will compute and return as follows:

0: The total fiber coupling. This is the product of the system efficiency and the receiver efficiency.

1: The system efficiency for fiber coupling.

2: The receiver efficiency for fiber coupling.

3: The total power.

4: The peak irradiance.

5, 6, 7: The pilot beam position, Rayleigh range, beam waist (x).

8, 9, 10: The pilot beam position, Rayleigh range, beam waist (y).

11, 12, 13: The local X, Y, Z coordinates of the center of the beam array on the end surface (this is a reference point and is not related to the amplitude of the beam).

21, 22: The X, Y coordinates of the centroid of the intensity distribution in local coordinates relative to the center of the beam. The orientation of the X/Y axes for this result are not necessarily the same as the orientation of the end surface.

23, 24, 25, 26: The X, Y beam width and X, Y M-squared values, respectively. For data 23, 24 with default Xtr1 value set to 0 beam widths are calculated in the lab coordinate system. When Xtr1 value set to 1 beam widths are calculated in the direction of its principle axes. Note when calculating M-squared value for asymmetric beams, the "Separate X, Y" must be checked when clicking the "Save" button in the POP analysis setting dialog. See "Beam width and M-squared".

27: The square root of second moment of the beam for x ², θ _x ², xθ _x, and xθ _y for Xtr1 values 0, 1, 2, and 3, respectively.

28: The square root of second moment of the beam for y ², θ _y ², yθ _y, and yθ _x for Xtr1 values 0, 1, 2, and 3, respectively.

29: The square root of second moment of the beam for xy and θ _x θ _y for Xtr1 values 0 and 1, respectively.

30, 31, 32: The mean, RMS and PTV irradiance variation, respectively, of the non-zero amplitude portion of the beam. These operands should only be used when the beam has nearly uniform irradiance and has just been clipped by a surface aperture.

33, 34, 35: The mean, RMS and PTV phase variation in radians, respectively, of the non-zero amplitude portion of the beam. These operands should only be used when the beam has nearly uniform irradiance and has just been clipped by a surface aperture.

40, 41, 42: The fraction of the total power enclosed within a circle of radius specified by the Xtr1 value in lens units, referenced to the beam centroid (40), chief ray (41), or surface vertex (42).

50, 51, 52: The radius in lens units of the circle at which the fraction of the total power enclosed is equal to the value specified by the Xtr1 value. The circle is centered on the beam centroid (50), chief ray (51), or surface vertex (52).

60, 61, 62, 63: The fiber coupling receiver efficiency amplitude and phase in radians for the Ex field (60 and 61) and the Ey field (62 and 63). These values do not consider system efficiency (see Data type 1 above). Data inputs 60-63 request a polarized POP calculation, but if the input beam is unpolarized, the field coupling efficiency amplitudes and phases are not physically well-defined.  Therefore, values of 0.0 will be returned if the input beam is unpolarized.

Undefined Data values will return 0.

The Xtr1 and Xtr2 values are only used by selected data numbers which are reserved for future expansion of this feature.If adjacent POPD operands all have the same Surf, Wave, Field, Xtr1, and Xtr2 values, then the POP analysis is done just once and all data returned at one time. Note the POPD operands must be on adjacent rows in the MFE for this efficiency to be implemented.

The options for the Data inputs are:

1 – RMS phase slope value over the surface.

2 – PV phase slope value over the surface.

3 – Minimum phase slope value over the surface.

4 – Maximum phase slope value over the surface.

5 – X coordinate for the point on the surface with the minimum phase slope value.

6 – Y coordinate for the point on the surface with the minimum phase slope value.

7 – X coordinate for the point on the surface with the maximum phase slope value.

8 – Y coordinate for the point on the surface with the maximum phase slope value.

9 – Value of the constant phase, if removed from the phase data.

10 – Value of the tilt about X, if removed from the phase data.

11 – Value of the tilt about Y, if removed from the phase data.

12 – Value of the power, if removed from the phase data.

The options for the Samp input are:

1 – 33 x 33 (default)

2 – 65 x 65

3 – 129 x 129

4 – 257 x 257

5 – 513 x 513

6 – 1025 x 1025

7 – 2049 x 2049

8 – 4097 x 4097

9 – 8193 x 8193

10 – 16385 x 16385

For Remove = 0 (default), no data is removed. For Remove = 1, any constant value at the vertex of the part is removed from the phase data before calculating the phase slope . For Remove = 2, the tilt term is removed from the phase data before calculating the phase slope. For Remove = 3, the power term is removed from the phase data before calculating the phase slope.

Orientation selects the direction of the slope calculation. Orientation = 0 (default) calculated along the tangential direction (radially outward). Orientation = 1 calculated along the sagittal direction (orthogonal to radially outward). Orientation = 2 calculated along the X-axis direction. Orientation = 3 calculated along the Y-axis direction. Orientation = 4 is the modulus, or full length of the slope vectors.

See also PSLP.

Global ray x-direction cosine of the ray after refraction from the surface defined by Surf at the wavelength defined by Wave.

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

The origin of the global coordinate system is at the global reference surface.

The curvature in lens units of the surface defined by Surf at the coordinate defined by X and Y, as measured in Lens Units within the coordinate system being used (see "Off-axis" below). This operand has mode, off-axis, remove, best-fit sphere (BFS), and Orientation flags.

• Mode = 0 to use Mech Semi-Dia and Mode = 1 (default) to use Clear Semi-Dia value displayed on the Lens Data Editor.
• Off-axis = 0 (default) the computation is calculated with respect to the system coordinates and Off-axis = 1 the computation is calculated with respect to a tilted and decentered coordinate system, where the origin of the coordinate system falls at the vertex of the off-axis part. The X and Y inputs will then refer to coordinates in the new off-axis coordinate system.
• Remove = 0 (default) no data is removed. Remove = 1 the base radius of curvature is removed from the data before calculation. Remove = 2 the best-fit sphere is removed from the data before calculation.
• BFS selects which type of best-fit sphere to remove from the data if Remove is set to 2. BFS = 0 (default) for minimum volume best-fit sphere. BFS = 1 for Minimum RMS best-fit sphere. BFS = 2 for Minimum RMS best-fit sphere with offset. BFS = 3 for Minimum volume best-fit sphere, reverse direction. The offset allows the calculation to shift the vertex of the BFS away from the data value at the vertex if it results in a lower RMS.
• Orientation selects the direction of the curvature calculation. Orientation = 0 (default) calculated along the tangential direction (radially outward). Orientation = 1 calculated along the sagittal direction (orthogonal to radially outward). Orientation = 2 calculated along the X-axis direction. Orientation = 3 calculated along the Y-axis direction. Orientation = 4 is the modulus or length of the curvature vector, at the orientation angle that contains the full length of the vector (The angle is not explicitly calculated and can vary between points on the curvature map).

The phase in waves at the primary system wavelength of the surface defined by Surf at the coordinate defined by X and Y, as measured in Lens Units. This operand has data and remove flags.

• Data = 0 (default) display the surface phase. Data = 1 display the tilt term within the phase when Remove is also set to 2. Data = 2 display the power term within the phase when Remove is also set to 3.

• Remove = 0 (default) no data is removed. Remove = 1 constant value at the vertex of the part is removed from the data . Remove = 2 the tilt term is removed from the data. Remove = 3 the power term is removed from the data.

Note that sampling is set to 33x33. See also DPHS.

The sag in lens units of the surface defined by Surf at the coordinate defined by X and Y, as measured in Lens Units within the coordinate system being used (see "Off-axis" below). This operand has mode, off-axis, remove, and best-fit sphere (BFS) flags.

• Mode = 0 to use Mech Semi-Dia and Mode = 1 (default) to use Clear Semi-Dia value displayed on the Lens Data Editor.

• Off-axis = 0 (default) the computation is calculated with respect to the system coordinates and Off-axis = 1 the computation is calculated with respect to a tilted and decentered coordinate system, where the origin of the coordinate system falls at the vertex of the off-axis part. The X and Y inputs will then refer to coordinates in the new off-axis coordinate system.

• Remove = 0 (default) no data is removed. Remove = 1 the base radius of curvature is removed from the data before calculation. Remove = 2 the best-fit sphere is removed from the data before calculation.

• BFS selects which type of best-fit sphere to remove from the data if Remove is set to 2. BFS = 0 (default) for minimum volume best-fit sphere. BFS = 1 for Minimum RMS best-fit sphere. BFS = 2 for Minimum RMS best-fit sphere with offset. BFS = 3 for Minimum volume best-fit sphere, reverse direction.

  The offset allows the calculation to shift the vertex of the BFS away from the data value at the vertex if it results in a lower RMS.

Note that sampling is set to 33x33. See also DSAG, SAGX, SAGY.

The slope in lens units of the surface defined by Surf at the coordinate defined by X and Y, as measured in Lens Units within the coordinate system being used (see "Off-axis" below). This operand has mode, off-axis, remove, best-fit sphere (BFS), and Orientation flags.

• Mode = 0 to use Mech Semi-Dia and Mode = 1 (default) to use Clear Semi-Dia value displayed on the Lens Data Editor.

• Off-axis = 0 (default) the computation is calculated with respect to the system coordinates and Off-axis = 1 the computation is calculated with respect to a tilted and decentered coordinate system, where the origin of the coordinate system falls at the vertex of the off-axis part. The X and Y inputs will then refer to coordinates in the new off-axis coordinate system.

• Remove = 0 (default) no data is removed. Remove = 1 the base radius of curvature is removed from the data before calculation. Remove = 2 the best-fit sphere is removed from the data before calculation.

• BFS selects which type of best-fit sphere to remove from the data if Remove is set to 2. BFS = 0 (default) for minimum volume best-fit sphere. BFS = 1 for Minimum RMS best-fit sphere. BFS = 2 for Minimum RMS best-fit sphere with offset. BFS = 3 for Minimum volume best-fit sphere, reverse direction.

  The offset allows the calculation to shift the vertex of the BFS away from the data value at the vertex if it results in a lower RMS.

• Orientation selects the direction of the slope calculation. Orientation = 0 (default) calculated along the tangential direction (radially outward). Orientation = 1 calculated along the sagittal direction (orthogonal to radially outward). Orientation = 2 calculated along the X-axis direction. Orientation = 3 calculated along the Y-axis direction. Orientation = 4 is the modulus or length of the slope vector, at the orientation angle that contains the full length of the vector (The angle is not explicitly calculated and can vary between points on the slope map).

Note that sampling is set to 33x33. See also DSLP.

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.