mtf

R2026b

Compute modulation transfer function of optical system

Since R2026b

Syntax

mtfr = mtf(opsys)

mtfr = mtf(opsys,Name=Value)

Description

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

mtfr = mtf(opsys) computes the modulation transfer function (MTF) for the optical system opsys using the default field points and wavelengths. The MTF represents contrast transfer as a function of spatial frequency in the image plane. The function computes MTF from a PSF generated for the specified field points and wavelengths.

mtfr = mtf(opsys,Name=Value) specifies options using one or more name-value arguments. For example, mtf(opsys,FieldPoints=fp,Wavelengths=587.56,Method="Huygens") computes a wave-optics MTF for the field point fp at a wavelength of 587.56 nanometers. The function uses these options to generate the PSF from which it computes the MTF.

Examples

Compute MTF at a Field Point

Load the sample Double Gauss lens system using zmximport. Define an off-axis field point at an angle of 3 degrees along the y-axis, and compute the geometric MTF for three distinct wavelengths (486.1 nm, 587.6 nm, and 656.3 nm).

opsys = zmximport("DoubleGaussLens.zmx");
fp = fieldPoint(Angles=[0 3]);
mtfr = mtf(opsys, FieldPoints=fp, Wavelengths=[486.1 587.6 656.3])

mtfr = 
  GeometricMTF with properties:

     Tangential: [1×1 struct]
       Sagittal: [1×1 struct]
     FieldPoint: [1×1 optics.fieldpoint.FieldAngle]
    Wavelengths: [486.1000 587.6000 656.3000]
      FFTLength: [128 128]

Compute and Plot Huygens MTF

Load the sample Double Gauss lens system using zmximport. Compute the Huygens MTF by setting the Method name-value argument to "Huygens". Limit the output curves to a spatial frequency of 150 cycles per millimeter using the MaximumFrequency argument, and specify an FFTLength of 512 to achieve higher frequency resolution.

opsys = zmximport("DoubleGaussLens.zmx");
mtfr = mtf(opsys, Method="Huygens", MaximumFrequency=150, FFTLength=512);

Visualize the tangential and sagittal contrast curves as a function of spatial frequency by passing the result object to the show function.

hmtf = show(mtfr)

hmtf = 
  MTFChart with properties:

               Legend: on
                 Grid: "off"
                Title: "Modulation Transfer Function"
                  MTF: [1×3 optics.result.HuygensMTF]
    WavelengthIndices: [1 2 3]
                Color: [3×3 double]
             Position: [0.0737 0.2521 0.8713 0.5977]
                Units: 'normalized'

  Show all properties

Query MTF Metrics

Load the sample Double Gauss lens system using zmximport. Compute the geometric MTF up to a maximum spatial frequency of 200 cycles per millimeter by setting the MaximumFrequency name-value argument.

opsys = zmximport("DoubleGaussLens.zmx");
mtfr = mtf(opsys, MaximumFrequency=200);

Use the frequencyAtContrast function to compute MTF50, the spatial frequency where the MTF first drops to 50% contrast. Then, use the contrastAtFrequency function to determine the exact sagittal and tangential contrast values at spatial frequencies of 30, 60, and 100 cycles per millimeter.

By default, these functions evaluate the entire optical system simultaneously and return multi-dimensional arrays. The dimensions map to [Fields, Wavelengths, Configurations, Planes] for the MTF50 output, and [Fields, Wavelengths, Frequencies, Planes] for the contrast output, where the rows represent field points and the columns represent wavelengths.

MTF50 = frequencyAtContrast(mtfr, 0.5)

MTF50 = 
MTF50(:,:,1,1) =

   22.2302   48.5808   37.1994
   30.4516   44.1749   35.1107
   26.2930   20.7316   19.6589


MTF50(:,:,1,2) =

   22.2300   48.5906   37.2039
   31.2080   43.8519   27.4440
   52.5096   33.6761   18.1949

contrast = contrastAtFrequency(mtfr, [30; 60; 100])

contrast = 
contrast(:,:,1,1) =

    0.4014    0.7605    0.6261
    0.5084    0.6298    0.5519
    0.4752    0.3834    0.3539


contrast(:,:,2,1) =

    0.2572    0.3637    0.2569
    0.1174    0.3793    0.2909
    0.3216    0.2569    0.2353


contrast(:,:,3,1) =

    0.1793    0.0742    0.2620
    0.0475    0.1648    0.0820
    0.2108    0.1898    0.1699


contrast(:,:,1,2) =

    0.4014    0.7606    0.6262
    0.5081    0.6205    0.4417
    0.7480    0.5750    0.3493


contrast(:,:,2,2) =

    0.2572    0.3639    0.2569
    0.2959    0.3558    0.1313
    0.4327    0.2412    0.2650


contrast(:,:,3,2) =

    0.1793    0.0742    0.2618
    0.0944    0.1362    0.1943
    0.0866    0.2809    0.2394

Input Arguments

opsys — Optical system

opticalSystem object

Optical system for which to compute the modulation transfer function, specified as an opticalSystem object.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: mtf(opsys,Method="Huygens",MaximumFrequency=150,FFTLength=512) computes a wave-optics MTF up to 150 cycles per millimeter using an FFT length of 512.

FieldPoints — Field points for MTF computation

opsys.FieldPoints (default) | FieldAngle object | FieldPosition object | array of FieldAngle or FieldPosition objects

Field points for the MTF computation, specified as a FieldAngle object, a FieldPosition object, or an array of field point objects. Each returned mtfr element contains the MTF for one field point.

By default, the FieldPoints value is the FieldPoints property of opsys.

Wavelengths — Wavelengths for MTF computation

opsys.Wavelengths (default) | M-element numeric vector

Wavelengths for MTF computation, specified as an M-element numeric vector. M is the number of wavelengths, and each element of the vector is a wavelength in nanometers. The returned MTF object contains tangential and sagittal curves for each specified wavelength.

Data Types: double

Method — MTF computation method

"Geometric" (default) | "Geometric" | "Huygens"

MTF computation method, specified as "Geometric" or "Huygens". This argument controls the internal PSF computation used to compute the MTF and the type of MTF result object returned.

Method	Description
"Geometric"	Compute the MTF from a geometric PSF. Use this method for fast analysis when aberrations are large compared to diffraction-limited performance.
"Huygens"	Compute the MTF from a Huygens PSF. Use this method when diffraction and phase effects are important.

ReferenceWavelengthIndex — Index of reference wavelength

positive integer

Index of the reference wavelength, specified as a positive integer. The reference wavelength is used to determine the chief ray hit position for centering the internal PSF used to compute the MTF.

If you specify Wavelengths and do not specify ReferenceWavelengthIndex, the function uses the index of the median wavelength after sorting the wavelength values. If you do not specify Wavelengths, the reference wavelength is specified by the PrimaryWavelengthIndex property of opsys.

MaximumFrequency — Maximum spatial frequency

diffraction-limited cutoff frequency (default) | nonnegative scalar

Maximum spatial frequency for the MTF curves, specified as a nonnegative scalar in cycles per millimeter. The function evaluates the tangential and sagittal MTF curves on a frequency grid from 0 to MaximumFrequency.

By default, the function uses the diffraction-limited cutoff frequency 1/(lambda*FNumber) at the primary wavelength.

Data Types: double

FFTLength — FFT size for MTF computation

PSFResolution (default) | positive integer scalar | 1-by-2 vector of positive integers

FFT size for computing the optical transfer function from the internal PSF, specified as a positive integer scalar or a 1-by-2 vector of positive integers. If you specify a scalar, the function uses the same FFT length for rows and columns. If you specify a vector, the first element is the number of rows and the second element is the number of columns.

The value of FFTLength must be greater than or equal to PSFResolution in each dimension. Larger values provide denser frequency sampling but do not change the maximum frequency.

Data Types: double

PSFResolution — Resolution of internal PSF image

[128 128] (default) | 1-by-2 vector of positive integers

Resolution of the internal PSF image used to compute the MTF, specified as a 1-by-2 vector of positive integers of the form [width height].

PSFPixelSize — Spatial sampling interval of internal PSF image

positive scalar

Spatial sampling interval of the internal PSF image in the image plane, specified as a positive scalar in microns. The internal PSF pixel size determines the spatial sampling used before the Fourier transform.

Data Types: double

Output Arguments

mtfr — Modulation transfer function results

array of optics.result.GeometricMTF objects | array of optics.result.HuygensMTF objects

Modulation transfer function results, returned as an array of optics.result.GeometricMTF objects when Method is "Geometric", or an array of optics.result.HuygensMTF objects when Method is "Huygens". The returned array contains one object for each field point specified by FieldPoints.

Each MTF object contains Tangential and Sagittal structures for the specified wavelengths. Each structure contains spatial frequency values in cycles per millimeter and corresponding MTF values.

The MTF result objects expose the Tangential, Sagittal, FieldPoint, Wavelengths, and FFTLength properties.

More About

Modulation transfer function

The modulation transfer function describes how an optical system transfers image contrast at different spatial frequencies. Higher MTF values indicate better contrast transfer at the corresponding spatial frequency.

The mtf function computes separate tangential and sagittal curves so you can compare contrast transfer along the principal image-plane directions.

Relationship to PSF

The mtf function computes the MTF from an internal point spread function (PSF). A narrower PSF generally corresponds to slower MTF rolloff and better contrast transfer at higher spatial frequencies.

MTF Computation

The mtf function computes MTF from the PSF of the optical system using Fourier analysis. The MTF describes contrast transfer as a function of spatial frequency and is returned separately for sagittal and tangential directions.

Version History

Introduced in R2026b