Modulation-transfer function

Bowden, The lithographic process the physics, in Introduction to Microlithography, 2nd ed., L.F. Thompson, C.G. Willson, and M.J. Bowden, Eds., p. 61, American Chemical Society, Washington, DC (1994). 

By convention, the MTF is normalized to unity at zero spatial frequency. At low spatial frequencies, the MTF is close to 1.0 (100%) it generally falls as the spatial frequency increases, until it reaches zero. Fligher spatial frequencies have lower contrast values than lower spatial frequencies. As spatial frequencies increase, the MTF curve falls until it reaches zero. This represents the limit of 

A concept that is related to MTF is the critical modulation transfer function (CMTF), which is a useful approximation for determining minimum modulation required for a photoresist. The minimum required modulation of a resist with (base 10) contrast y is expressed as  

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The detectability of critical defects with CT depends on the final image quality and the skill of the operator, see figure 2. The basic concepts of image quality are resolution, contrast, and noise. Image quality are generally described by the signal-to-noise ratio SNR), the modulation transfer function (MTF) and the noise power spectrum (NFS). SNR is the quotient of a signal and its variance, MTF describes the contrast as a function of spatial frequency and NFS in turn describes the noise power at various spatial frequencies [1, 3]. 

Modulation Transfer Function MTF The course of the MTF is calculated from the established inherent unsharpness. 

The unsharpness is generally measured with the duplex wire IQI (CERL B), strip pattern IQI-s (here we used a Siemens star) or adduced via the modulation transfer function (MTF). References [1,2,3] give the MTF s determined for the BAS2000, BAS2500 and BAS5000. 

LVSEM low-voltage scanning electron microscope MTF modulation transfer function... 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

Different values of will result if the integral limits (i.e., band width) or modulation transfer function in the integral change. All surface characterization instruments have a band width and modulation transfer function. If rms roughness values for the same surface obtained using different instruments are to be compared, optimally the band widths and modulation transfer functions would be the same they should at least be known. In the case of isotropic surface structure, the spatial frequencies p and q are identical, and a single spatial frequency (/>) or spatial wavelength d= /p) is used to describe the lateral dimension of structure of the sample. 

The modulation transfer function of the optical scatterometer is nearly unity. The spatial frequency band width, using 0.633-nm photons from a He-Ne laser, is typically 0.014—1.6 jim corresponding to a spatial wavelength band width 70— 0.633 pm. This corresponds to near normal sample illumination with a minimum... 

The significance of instrument band width and modulation transfer function was discussed in connection with Equation (3) to characterize the roughness of nominally smooth surfaces. The mechanical (stylus) profilometer has a nonlinear response, and, strictly speaking, has no modulation transfer function because of this. The smallest spatial wavelength which the instrument can resolve, 4nin> given in terms of the stylus radius rand the amplitude aoi the structure as... 

R, D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R, McNeil, and J. M. Bennett. Microstructure Characterization by Angle-Resolved Scatter and Comparison to Measurements Made by Other Techniques. To be published in AppL Opt. This work discusses the band width and modulation transfer function of the scatterometer, stylus profilometer, optical pro-filometer, and total integrated scattering systems, and gives results of mea suring several surhices using all techniques. 

Figure 2b. Profiles of the modulation transfer function (MTF), its inverse and Wiener inverse-filter.

Modulation transfer function (MTF) analyses, 19 222, 264-265 Module factor investment cost estimates, 9 530... 

Resolution is set by the numerical aperture of the lens and by the wavelength of the exposing radiation. Contrast at a given resolution is typically assumed to be given by the modulation transfer function (M.T.F.), where... 

Figure 2. Modulation Transfer Functions (MTF s) for the Perkin Elmer Micralign cameras operating at 250 nm, 300 nm and 400 nm, and for a step-and-repeat camera lens with a numerical aperture of 0.35.

Plomp, 1988] Plomp, R. (1988). The negative effect of amplitude compression in multichannel hearing aids in the light of the modulation-transfer function. J. Acoust. Soc. Am., 83 2322-2327. 

The MTF (modulation transfer function derived by plotting the video amplitude versus the number of lines) should be comparable to that of an ideal Gaussian Spot with diameter 1/500 of the image width. 

The ultimate resolution that can be obtained with a Vidicon-tube system can best be seen from the manufacturers specification. The spatial resolution is expressed by the so called modulation-transfer function (MTF), which is measured by the projection of a test mask directly on the photocathode, with visible light. Of course, this test does not include the degradation by the phosphor screen in X-ray applications. 

Equal modulation transfer function (MTF) across the array. 

SIT ISIT. The resolution of SIT detectors can be defined in several ways— a) position (spatial) resolution, b) Rayleigh resolution, and c) modulation transfer function (MTF). 

Another means of expressing the fidelity of an optical system is in terms of its modulation transfer function. The modulation transfer function describes the ability of the optical system to accurately reproduce an object whose pattern of luminance varies in a sinusoidal manner. An optical system which can precisely duplicate the modulation pattern of the object in the modulation pattern of the image has a modulation transfer function equal to 1.0 this represents the performance of a perfect system. The greater the difference between the modulation pattern in the image compared with that in the object, the lower the modulation transfer function. In practice, the modulation transfer pattern is usually evaluated with a square-wave pattern produced by a periodic array of lines. The modulation transfer function approaches zero as the spatial frequency of the lines increases. The limiting resolution in terms of the modulation transfer function is... 

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