contrastAtFrequency

R2026b

Compute MTF contrast at spatial frequencies

Since R2026b

Syntax

contrast = contrastAtFrequency(mtfr,frequencies)

Description

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

contrast = contrastAtFrequency(mtfr,frequencies) returns the modulation transfer function (MTF) contrast at each spatial frequency in frequencies. The function returns sagittal and tangential contrast values for each MTF object, wavelength, and requested frequency.

Examples

Compute Contrast at Specific Spatial Frequencies

Load the sample Double Gauss lens system using zmximport. Compute the geometric MTF up to a maximum evaluation frequency of 200 cycles/mm to ensure the generated spatial curves safely enclose all test frequencies of interest.

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

Define a vector of spatial frequencies representing standard imaging performance checkpoints (e.g., 30, 60, and 100 cycles/mm). Query the exact contrast values preserved by the lens system at these boundaries using the contrastAtFrequency method.

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

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

    0.4013    0.7605    0.6261
    0.5085    0.6298    0.5518
    0.4754    0.3834    0.3537


contrast(:,:,2,1) =

    0.2571    0.3638    0.2569
    0.1174    0.3794    0.2909
    0.3216    0.2569    0.2353


contrast(:,:,3,1) =

    0.1791    0.0741    0.2619
    0.0474    0.1648    0.0822
    0.2109    0.1898    0.1700


contrast(:,:,1,2) =

    0.4014    0.7606    0.6262
    0.5081    0.6204    0.4416
    0.7480    0.5750    0.3491


contrast(:,:,2,2) =

    0.2571    0.3639    0.2569
    0.2959    0.3558    0.1312
    0.4328    0.2413    0.2649


contrast(:,:,3,2) =

    0.1792    0.0741    0.2618
    0.0945    0.1361    0.1943
    0.0867    0.2809    0.2393

The resulting array contains multi-dimensional data spanning field points, wavelengths, frequencies, and orientations. To analyze orientation-dependent performance (such as astigmatism), slice the 4th dimension to isolate the sagittal and tangential contrast matrices.

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

sagittalContrast = 
sagittalContrast(:,:,1) =

    0.4013    0.7605    0.6261
    0.5085    0.6298    0.5518
    0.4754    0.3834    0.3537


sagittalContrast(:,:,2) =

    0.2571    0.3638    0.2569
    0.1174    0.3794    0.2909
    0.3216    0.2569    0.2353


sagittalContrast(:,:,3) =

    0.1791    0.0741    0.2619
    0.0474    0.1648    0.0822
    0.2109    0.1898    0.1700

tangentialContrast = contrast(:, :, :, 2)

tangentialContrast = 
tangentialContrast(:,:,1) =

    0.4014    0.7606    0.6262
    0.5081    0.6204    0.4416
    0.7480    0.5750    0.3491


tangentialContrast(:,:,2) =

    0.2571    0.3639    0.2569
    0.2959    0.3558    0.1312
    0.4328    0.2413    0.2649


tangentialContrast(:,:,3) =

    0.1792    0.0741    0.2618
    0.0945    0.1361    0.1943
    0.0867    0.2809    0.2393

Input Arguments

mtfr — Modulation transfer function results

GeometricMTF object | HuygensMTF object | array of GeometricMTF or HuygensMTF objects

Modulation transfer function results, specified as a GeometricMTF object, a HuygensMTF object, or an array of MTF result objects. Create these objects by using the mtf object function.

When you specify an array of MTF result objects, all objects in the array must use the same wavelengths.

frequencies — Spatial frequencies at which to compute contrast

finite, nonnegative real scalar | column vector of finite, nonnegative real values

Spatial frequencies at which to compute MTF contrast, specified as a finite, nonnegative real scalar or column vector of finite, nonnegative real values. Units are in cycles per millimeter.

Data Types: double

Output Arguments

contrast — MTF contrast values

N-by-M-by-K-by-2 numeric array

MTF contrast values, returned as an N-by-M-by-K-by-2 numeric array. N is the number of MTF objects in mtfr, M is the number of wavelengths, K is the number of frequencies in frequencies, and the fourth dimension stores the sagittal and tangential directions.

The first page in the fourth dimension, contrast(:,:,:,1), contains sagittal contrast values. The second page, contrast(:,:,:,2), contains tangential contrast values.

Values are contrast fractions from 0 to 1. A value of 1 indicates full contrast transfer, and a value of 0 indicates no contrast transfer at the corresponding spatial frequency.

For requested frequencies above the maximum stored frequency in the MTF data, the corresponding contrast value is 0. If an MTF object contains empty MTF data, the corresponding contrast values are NaN.

Data Types: double

Version History

Introduced in R2026b