Paraxial

Paraxial information, including cardinal points, of optical system

Since R2026a

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    Description

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

    A Paraxial object stores the paraxial information that characterizes an optical system, including its six cardinal points – two focal, two principal, and two nodal points. In the paraxial approximation, the entrance and exit pupil is considered in terms of paraxial rays.

    Creation

    To create a Paraxial object, use the paraxialInfo function. For example, info = paraxialInfo(opsys) computes the paraxial information for the optical system opsys and returns it as the Paraxial object info.

    Properties

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    Wavelengths at which the paraxial information has been computed, specified as a positive numeric scalar . By default, the paraxialInfo function computes the paraxial information at the primary wavelength of the optical system opsys, represented as opsys.Wavelengths(opsys.PrimaryWavelengthIndex).

    F-number of the optical system, specified as a positive numeric scalar. An f-number in an optical system is a ratio that represents the relationship between the focal length of a lens and the diameter of its aperture. It is calculated by dividing the focal length by the aperture diameter. You can use it to measure the amount of light that can pass through the lens.

    Sine of the angle between the optical axis and the marginal ray in the image plane, specified as a positive numeric scalar. The NumericalAperture value characterizes the range of angles over which an optical system can accept or emit light.

    Focal length of the optical system, specified as a numeric scalar. The focal length is the distance between the second principal point and the second focal point. This is also referred to as the effective focal length.

    Data Types: double

    Distance between the back vertex of the last component and the second focal point, specified as a numeric scalar.

    Point of ray convergence, specified as a 3-element row vector. The vector is in the form [x y z], where the x-, y-, and z-coordinates represent the location of the point at which rays traveling from the image space to the object space converge on the optical axis.

    Data Types: double

    First principal point, specified as a 3-element row vector. The vector is in the form [x y z], where the x-, y-, and z-coordinates represent the location of the point at which the first principal plane intersects the optical axis. If you trace rays from the object space to the image space, the first principal plane is the plane where the extensions of the refracted rays, after passing through the lens, appear to diverge from, as if they originated from this plane.

    Data Types: double

    Second principal point, specified as a 3-element row vector. The vector is in the form [x y z], where the x-, y-, and z-coordinates represent the location of the point at which the second principal plane intersects the optical axis. If you trace rays from the image space to the object space, the second principal plane is the plane where the extensions of the refracted emergent rays appear to originate.

    Data Types: double

    Radius of the paraxial entrance pupil, specified as a positive scalar. The entrance pupil is the limiting aperture that determines the amount of light entering the system.

    Global position of the paraxial entrance pupil, specified as a 3-element row vector.

    Data Types: double

    Orientation of the entrance pupil, specified as a 3-element row vector. The orientation value is the unit vector normal to the surface of the paraxial entrance pupil.

    Data Types: double

    Radius of the paraxial exit pupil, specified as a positive scalar. The exit pupil is a virtual aperture in the optical system through which rays can exit the system.

    Global position of the paraxial exit pupil, specified as a 3-element row vector.

    Data Types: double

    Length of the axial path, specified as a positive scalar. This value represents the length of the optical system along the optical axis from the front vertex of the first surface to the back vertex of the last non-image surface.

    Examples

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    This example uses:

    Open Live Script

    Create an optical system that contains a photo zoom lens using the createPhotoZoom helper function. The function is attached to this example as a supporting file.

    opsys = createPhotoZoom;

    Compute the paraxial information for the optical system using the paraxialInfo object function.

    info = paraxialInfo(opsys)
    info = 
  Paraxial with properties:

               Wavelength: 558
                  FNumber: 2.9212
        NumericalAperture: 0.1687
              FocalLength: 72.0158
          BackFocalLength: 39.0209
          FirstFocalPoint: [0 0 -3.1518]
         SecondFocalPoint: [0 0 182.7418]
      FirstPrincipalPoint: [0 0 68.8640]
     SecondPrincipalPoint: [0 0 110.7259]
      EntrancePupilRadius: 12.3265
    EntrancePupilPosition: [0 0 72.3885]
          ExitPupilRadius: 11.5534
        ExitPupilPosition: [0 0 115.1765]
          AxialPathLength: 143.7209

    Display the back focal length, which is the distance between the final surface and the point at which rays converge.

    disp("Back Focal Length = " + info.BackFocalLength)
    Back Focal Length = 39.0209

    More About

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    Version History

    Introduced in R2026a

    See Also

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