Surface

R2026b

Optical surface properties

Since R2026a

Description

Add-On Required: This feature requires the Optical Design and Simulation Library for Image Processing Toolbox add-on.

A Surface object specifies the properties of a surface in an optical system, such as its shape and radius of curvature.

Creation

Create a Surface object using these options.

• Use the addRefractiveSurface object function. Use this function to add at least two refractive surfaces, which constitute a lens element, as the next component of an optical system. You can specify their properties, such as shape, material, and aspheric coefficients, using name-value arguments. When you add two or more surfaces using addRefractiveSurface, you create a LensElement object.

• Use the addDiaphragm object function. Use this function to add a diaphragm, which contains a surface, as the next component to an optical system. You can specify its properties, such as shape and semi-diameter, using name-value arguments.

• Use the addMirror object function. Use this function to add a mirror, which contains a surface, as the next component to an optical system. You can specify its properties, such as shape, radius, and aspheric coefficients, using name-value arguments.

• Use the addImagePlane object function. Use this function to add an image plane, which contains a surface, as the next component to an optical system. You can specify its properties, such as semi-diameter, using name-value arguments.

• Use the addImageSensor object function. Use this function to add an image sensor, which contains a surface, as the next component to an optical system. You can specify its properties using name-value arguments.

• Use the optics.surface.Surface function described here. Use this function when you want to create a surface without adding it to the optical system, or modify the properties of a surface already in the system. After creating the object, you can specify the surface properties by modifying the properties of the object.

Syntax

rsurf = optics.surface.Surface

rsurf = optics.surface.Surface(PropertyName=Value)

Description

rsurf = optics.surface.Surface creates a Surface object with default properties.

rsurf = optics.surface.Surface(PropertyName=Value) sets writeable properties using one or more name-value arguments.

Example: optics.surface.Surface(Radius=10) creates a Surface object representing a surface with a radius of 10.

Properties

Name — Name of surface

"" (default) | scalar | character vector

Name of the surface, specified as a scalar or character vector.

Radius — Radius of curvature

0 (default) | numeric scalar | 2-element row vector

Radius of curvature of the surface, specified as one of these options:

• Numeric scalar — The radius of curvature applies in both the x- and y-directions.

• 2-element row vector — Specifies the radius of curvature for a biconic surface, in the form [R_x, R_y], where R_x and R_y are the radii of curvature in the x- and y-directions, respectively.

Aspherics — Aspheric coefficients

zeros(1,20) (default) | 20-element row vector

Aspheric coefficients describing the aspheric profile of the surface, specified as a 20-element row vector. By default, both even-powered and odd-powered aspheric coefficients are equal to zero, and the surface is spherical. The conic surface shape depends on the magnitude and sign of the conic constant specified by the ConicConstant property.

EvenAspherics — Even-powered aspheric coefficients

zeros(1,10) (default) | 10-element row vector

Even-powered aspheric coefficients describing the aspheric profile of the surface, specified as a 10-element row vector.

ConicConstant — Conic constant

0 (default) | numeric scalar | 2-element row vector

Conic constant that defines the conic shape of the aspheric surface profile, specified as one of these options:

• Numeric scalar — The conic constant applies in both the x- and y-directions.

• 2-element row vector — Specifies the conic constant for a biconic surface, in the form [K_x, K_y], where K_x and K_y are the conic constants in the x- and y-directions, respectively.

Depending on the value of the conic constant K, the aspheric surface has these conic shapes. For a biconic surface, the conic shape in each direction is determined independently by the corresponding element of ConicConstant.

ConicConstant (K) Value	Conic Shape
K = 0	Sphere
K in range [-1,0]	Ellipse
K = -1	Parabola
K in range [-inf,-1]	Hyperbola

NormalizationRadius — Normalization radius

1 (default) | positive scalar

Normalization radius, specified as a positive scalar. The normalization radius is used to non-dimensionalize the higher-order terms in the polynomial describing the aspheric surface.

Grid — Additional Z-sag values on the regular grid

[] (default) | M-by-N matrix

Additional Z-sag values on the regular grid, specified as an M-by-N matrix. Units are in millimeters. M is the number of y samples spanning GridYLims, and N is the number of x samples spanning GridXLims.

The object adds these grid values to the existing surface sag value. Positive values move the surface toward the positive z direction and negative values move the surface toward the negative z direction from the baseline that the object computes using the Radius, ConicConstant, and aspheric term properties in local surface coordinates. The object interpolates grid values using bicubic interpolation and extrapolates values near the edges.

The element Grid(1,1) corresponds to the corner at (GridYLims(1), GridXLims(1)), which is the minimum y- and minimum x-position of the grid. The element Grid(1,end) corresponds to (GridYLims(1), GridXLims(2)), and Grid(end,end) corresponds to (GridYLims(2), GridXLims(2)), which is the maximum y- and maximum x-position of the grid. Row index increases with y, and column index increases with x.

Data Types: double

GridXLims — X-limits of grid edges

2-element row vector

X-limits of the grid edges in local surface coordinates, specified as a 2-element row vector. Units are in millimeters. The vector is of the form [x_min x_max], where x_min and x_max are the minimum and maximum x-coordinates of the grid, respectively. The second element must be greater than the first.

By default, the limits are [–sd sd] for circular shapes and [–w/2 w/2] for rectangular shapes, where sd is the semi-diameter and w is the width of the rectangular surface. The object ignores grid values that extend outside the surface shape. Valid regions of the surface not included in these limits use a grid value of 0.

Data Types: double

GridYLims — Y-limits of grid edges

2-element row vector

Y-limits of the grid edges in local surface coordinates, specified as a 2-element row vector. Units are in millimeters. The vector is of the form [y_min y_max], where y_min and y_max are the minimum and maximum y-coordinates of the grid, respectively. The second element must be greater than the first.

By default, the limits are [–sd sd] for circular shapes and [–h/2 h/2] for rectangular shapes, where sd is the semi-diameter and h is the height of the rectangular surface. The object ignores grid values that extend outside the surface shape. Valid regions of the surface not included in these limits use a grid value of 0.

Data Types: double

Shape — Shape of surface

Circular object (default) | Rectangular object

Shape of the surface, specified as one of these options.

• Circular object — Circular surface shape.

• Rectangular object — Rectangular surface shape.

By default, the shape of the surface is circular, with a semi-diameter of 1.

Coating — Optical coating

opticalCoating object

Optical coating applied to the surface, represented as an opticalCoating object. By default, the coating is applied to the front of the surface. To specify whether to apply the coating to the front, back, or both parts of lens surfaces, use the CoatingSide name-value argument of the addCoating function.

Position — Position of surface

[0 0 0] (default) | 3-element row vector

Position of the first vertex of the surface, specified as a 3-element row vector. The vector is in the form [x y z], where each element is the x-, y-, and z-coordinate in the local coordinate system of the component that contains the surface.

To learn more about the local component coordinate system, see Coordinate Systems in Optics.

TiltAngles — Tilt angles of surface

[0 0 0] (default) | 3-element row vector

Tilt angles of the surface, specified as a 3-element row vector. The vector is in the form [$${\theta }_x$$ $${\theta }_y$$ $${\theta }_z$$], where $${\theta }_x$$, $${\theta }_y$$, and $${\theta }_z$$ are tilt angles with respect to the x, y, and z-axes, respectively, of the local coordinate system of the component that contains the surface.

To learn more about the local component coordinate system, see Coordinate Systems in Optics.

Note

The TiltAngles property represents Euler angles. If you specify angles that are multiples of 90 degrees, visually verify the orientation of the optical system. Gimbal lock can occur, in which two of the three rotational axes become aligned. This alignment results in the loss of one degree of freedom, and can lead to ambiguous or unintended orientations.

Examples

Create Refractive Surfaces

Create an empty optical system.

opsys = opticalSystem(Name="Lens");

Create two lens surfaces using the optics.surface.Surface function. Specify the radius of curvature of the surfaces using the Radius property.

surf1 = optics.surface.Surface(Radius=2);
surf2 = optics.surface.Surface(Radius=-2);

Create a LensElement object, which represents a lens element, using the optics.component.LensElement function. Specify the two lens surfaces to the Surfaces property of the component object. Specify the thickness of the lens as 2.5 millimeters using the Thickness property of the LensElement object.

lens = optics.component.LensElement(Surfaces=[surf1,surf2],Thickness=2.5)

lens = 
  LensElement with properties:

          Name: [0×0 string]
     Materials: [1×1 opticalMaterial]
     Thickness: 2.5000
      Surfaces: [1×2 optics.surface.Surface]
         Shape: [1×2 optics.shape.Circular]
      Coatings: [0×0 opticalCoating]
      Position: [0 0 0]
    TiltAngles: [0 0 0]

Add the lens element component to the optical system using the add function.

add(opsys,lens)

Display a 2-D visualization of the optical system using the view2d function.

view2d(opsys)

ans = 
  OpticalSystemViewer2D with properties:

            Title: ""
    OpticalSystem: [1×1 opticalSystem]
           Labels: "none"
      FieldPoints: "on"
             Rays: [0×0 optics.ui.Rays2D]
           Parent: [1×1 Figure]

  Show all properties

Version History

Introduced in R2026a

R2026b: Specify biconic surface properties

You can now specify separate radii of curvature and conic constants in the x- and y-directions to create biconic surfaces by using the Radius and ConicConstant properties, respectively.

R2026b: Specify grid sag values for surface

You can now specify additional Z-sag values on a regular grid to add to the surface sag baseline by using the Grid, GridXLims, and GridYLims properties.