MFT measurement using a Shack-Hartmann wavefront sensor

The Modulation Transfer Function or MTF measurement is a crucial metrology technique to evaluate how an object’s contrast is captured after passing through an optical system as a function of spatial frequency. It is a critical criterion especially for imaging systems, as it allows you to judge the imaging quality in terms of spatial frequency response. Thus, the MTF is always plotted compared to the case of a diffraction limited optical system (see Figure 1).

The closer to the diffraction limit the optical system is, the less it has aberrations.


Figure 1 : Modulation Transfer Function. The spatial frequency is given in cy/mm (cycles per millimeter)

As MTF is a quantitative and standardized way to characterize optical systems, this measurement is used by optical engineers and designers in order to: 


    • Characterize a lens, a mirror, or a complex optical system like a telescope

    • Compare actual performance of an optical system to an optical design

The MTF measurement can be processed from the phase via double fourier transform. In addition to that, the Shack-Hartmann provides a 2D measurement of the phase in one acquisition and so the Shack-Hartmann provides an instantaneous 2D-MTF measurement offering access to every azimuthal angle. 

In this article we present a MTF measurement done with the HASO Shack-Hartmann wavefront sensors by Imagine Optic, a company renowned for its expertise in optical metrology instrumentation for over 25 years. It is combined with the RFLEX tool to have an easier wavefront measurement by double pass as it integrates the light source.

A wavefront measurement with a HASO sensor is performed to an accuracy of the order of λ/100rms and consequently the MTF calculation is performed with an accuracy of less than 1 point (1%), which cannot be achieved by any chart-based measuring instrument. 

Moreover, this measurement solution allows convenient implementation allowing on-axis and off-axis measurements.

Figure 2: Characterize an optic using Shack-Hartmann wavefront sensor 

Here is a setup example used to measure the MTF of a lens with a 1.5µm light source:


Once the measurement is done, the software developed by Imagine Optic, Waveview4, computes the wavefront and the MTF. 

On the screenshot below, we can clearly see that this optical system on Figure 2 has aberrations. Indeed, the wavefront is not uniform and the MTF curve (solid line) is not close to the diffraction limit (dotted line). 


Figure 3: WaveView4 screen: MTF and wavefront visualization

For a deeper analysis, WaveView4 can also compute the Point Spread Function (PSF), wavefront aberrations and Zernike or Legendre polynomials. 

Note that the HASO R-FLEX instrument use can be extended to the characterization of large optics once combined with a third accessory,  the LA module for the R-FLEX2.

The trio, called the Optical Engineer Companion (OEC) is fully customizable (wavelength, aperture, resolution…) and that’s why Imagine Optic nicknamed it the “Swiss-Knife of metrology”.

The OEC is now available with the LIFT technology, which increases the resolution by a factor of 16.

For the full line of Imagine Optic wavefront sensors, click HERE.

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