Sensor Modulation Transfer Function Research Articles

Fast full-field modulation transfer function analysis for photographic lens quality assessment.

Full-field modulation transfer function (MTF) data based on the slanted-edge method can give useful insights on the performance of a photographic lens sample and its shortcomings. Decentering and other out-of-tolerance states are recognized easily. A process to derive accurate lens MTF from slanted-edge spatial frequency response measurements is presented, covering chart design and alignment, data capture by standard digital cameras, slanted-edge algorithm implementation requirements, sensor and chart MTF corrections, and also visualization of the results. It is demonstrated that the reliability of the measured MTF values is by far good enough to support automated quality assessment with a measurement accuracy of ≈0.02 MTF and repeatability of ≲0.005 up to 100 c/mm. The measured full-field MTF values provide an unambiguous numerical criterion for comparison with expectations based on lens design.

Endorectal digital prostate tomosynthesis (endoDPT): a proof-of-concept study

In this study we present endorectal digital prostate tomosynthesis (endoDPT), a proposed method of high resolution prostate imaging using an endorectal x-ray sensor and an external x-ray source. endoDPT may be useful for visualizing the fine detail of small structures such as low dose rate brachytherapy (LDRBT) seeds that are difficult to visualize with current methods. The resolution of endoDPT was characterized through measurement of the modulation transfer function (MTF) and artifact spread function (ASF) in computational and physical phantoms. The qualitative resolution of endoDPT was assessed relative to computed tomography (CT) through imaging of LDRBT seeds implanted in ex vivo canine prostates. The x-ray sensor MTF reached 10% at 11.50 mm−1, the reconstruction algorithm MTF reached a maximum at 7.08 mm−1, and the ASF was 2.5 mm (full-width at half-maximum). Fine structures in LDRBT seeds like the 0.05 mm thick shell were visible with endoDPT but not CT. All endoDPT images exhibited an overshoot artifact. The measured MTFs were consistent with other studies using similar x-ray sensors and demonstrated improved resolution compared to digital breast tomosynthesis; this result was due to the smaller endoDPT x-ray sensor detection element size and quantitatively demonstrates the high resolution of endoDPT. The ASF demonstrated worse depth resolution compared to in-plane resolution, due to partial angular sampling; partial angular sampling also caused the observed overshoot artifact in the endoDPT images. However, endoDPT still was able to visualize fine structures such as the LDRBT seed shell to a much higher degree than CT. This high-resolution visualization may be useful for improvements in patient specific LDRBT dosimetry. Overall, these results indicate endoDPT is capable of high in-plane spatial resolution and is thus well poised for optimization and studies assessing clinical utility.

Contrast computation methods for interferometric measurement of sensor modulation transfer function

Accurate measurement of image-sensor frequency response over a wide range of spatial frequencies is very important for analyzing pixel array characteristics, such as modulation transfer function (MTF), crosstalk, and active pixel shape. Such analysis is especially significant in computational photography for the purposes of deconvolution, multi-image superresolution, and improved light-field capture. We use a lensless interferometric setup that produces high-quality fringes for measuring MTF over a wide range of frequencies (here, 37 to 434 line pairs per mm). We discuss the theoretical framework, involving Michelson and Fourier contrast measurement of the MTF, addressing phase alignment problems using a moiré pattern. We solidify the definition of Fourier contrast mathematically and compare it to Michelson contrast. Our interferometric measurement method shows high detail in the MTF, especially at high frequencies (above Nyquist frequency). We are able to estimate active pixel size and pixel pitch from measurements. We compare both simulation and experimental MTF results to a lens-free slanted-edge implementation using commercial software.

Full-Scale Assessment of Pansharpening Through Polynomial Fitting of Multiscale Measurements

Pansharpening techniques aim at improving the spatial resolution of a multispectral data set (MS) by using a panchromatic image (Pan) acquired on the same scene with a greater spatial resolution and consequently a lower ground sample distance (GSD). Usually, a quantitative assessment of the fused products cannot be directly performed because of the lack of a reference MS data set with the same GSD of the Pan. A well-known solution is Wald's protocol: The original MS and Pan are spatially degraded, the reducing factor being the ratio between their GSDs. Pansharpening is then performed between the reduced MS and Pan data sets, and the fused products are compared with the original MS, which can be used as reference. In this protocol, fusion performances are assumed to be independent of the scale so that the results at the reduced scale are an estimation of those at the original resolution. This hypothesis can be more or less reliable, depending on the sensor and/or the scene content. The objective of this paper is to propose a new methodology to infer the unknown performances of a pansharpening method at full scale. For this purpose, multiple sets of fused images are computed at degraded scales by downsampling Pan and MS data sets by means of the sensor modulation transfer function. Multiscale quality/distortion measurements are fitted by linear and quadratic polynomials in order to extrapolate their full-scale values. Once the proposed protocol has been assessed in the presence of reference originals, the obtained results are extended to the case where the reference image is not available.

One-dimensional sensor modulation transfer function, revisited

In this theoretical study the modulation transfer function (MTF) of an ideal one-dimensional image sensor array is calculated using computer simulations and simple mathematical concepts. These calculations take into account the finite size of the pixels, the discrete and periodic arrangement of the pixels, and the effect of the phase shift between the pixel array and the signal incident on the imager. It is found that the actual MTF of the sensor is more feature rich than implied by the Sinc function. In particular, when imaging periodic patterns on the sensor, for example to measure the resolution, phase shift between the incident pattern and the sensor and the spatial frequency can dramatically affect the results. An exact formula for the phase averaged MTF is derived.

Theoretical Models of Modulation Transfer Function, Quantum Efficiency, and Crosstalk for CCD and CMOS Image Sensors

This paper proposes analytical models of modulation transfer function (MTF), quantum efficiency (QE), and crosstalk for charge-coupled device (CCD) and CMOS image sensors. A unified MTF model for a CCD sensor built on an epitaxial layer deposited on a highly doped substrate was developed by Stevens. The Stevens model uses sinusoidal illumination to calculate the sensor MTF degradation due to charge diffusion and sampling aperture as a function of spatial frequency. The drawback of this approach is the difficulty to evaluate analytically the electrical crosstalk distribution, which can be a good tool for predicting the detector performances, particularly for smaller pixels. In this paper, we use point-source illumination to evaluate the pixel response function (PRF). This approach is applied to the case of CMOS sensors and buried channel CCD sensors. The MTF model includes the impact of pixel size and charge diffusion. The QE model and crosstalk distribution are directly derived from the PRF expression. The models can take into account an electric field induced by a doping gradient.

Sensor modulation transfer function measurement using band-limited laser speckle

A new methodology for image sensor modulation transfer function measurement using band-limited laser speckle is presented. We use a circular opal milk glass diffuser illuminated by a 5 mW He-Ne laser and a linear polarizer to generate band-limited speckle on the sensor. The power spectral density cut-off frequency of the speckle is chosen to be twice that of the sensor Nyquist frequency by placing the sensor at the specific Z location along the optical axis. For the speckle input, we calculate the power spectral density at the sensor using the Rayleigh-Sommerfeld integral and then measure the output power spectral density for the speckle pattern captured by the sensor. With these data, the two-dimensional image sensor modulation transfer function (MTF) is calculated.

Unified MTF for scintillator-coupled CMOS sensor

The spatial resolution of scintillator-coupled CMOS sensor has been investigated from intrinsic sensor Modulation Transfer Function (MTF) to system MTF for the conditions of the digital radiography. For the intrinsic sensor MTF, the geometric MTF (gMTF) and the unified MTF (uMTF) were compared by analytic calculations for various pixel sizes. The effects of the initial dark signal of the sensor were considered in the calculation of the uMTF and reflected in a newly developed semi-empirical model. The measured system MTF and the calculated system MTF including semi-empirical model were compared under radiography conditions of 28 and 80 kVp. From the results, the calculated system MTF reflecting the dark-signal contribution on the sensor resolution did fit for the measured system resolution, and the higher the fraction of an initial dark signal to an output signal in response to X-ray exposure showed more degradation of the system resolution even with same scintillator and sensor.

CMOS APS MTF modeling

In this paper, a unified model, based on a thorough analysis of experimental data, is developed for the overall modulation transfer function (MTF) estimation for CMOS image sensors. The model covers the physical diffusion effect together with the influence of the pixel active area geometrical shape. Comparison of both our predicted results and the MTF calculated from the point spread function (PSF) measurements of an actual pixel array gives excellent agreement. This confirms the hypothesis that the active area shape together with the photocarrier diffusion effect are the determining factors of the overall CMOS active pixel sensor (APS) MTF behavior, and allows us to extract the minority-carrier diffusion length. The results indicate that for any potential active area shape, a reliable estimate of image performance is possible, so the tradeoff between the conflicting requirements, such as signal-to-noise ratio (SNR) and MTF could be compared per pixel design.

A unified model of carrier diffusion and sampling aperture effects on MTF in solid-state image sensors

A unified model is used for calculating the modulation-transfer function (MTF) of a front-side-illuminated, solid-state image sensor including the effects of lateral diffusion of charge carriers within the substrate and less than full pixel sampling apertures. Moreover, it is found that, in general, these two effects cannot be treated independently and then combined, using the convolution theorem to arrive at the total sensor MTF as has often been done in the past. It is found that the actual MTF is higher than predicted by simply multiplying the diffusion and aperture MTFs together. This discrepancy is seen to increase as pixel-to-pixel crosstalk increases for a given aperture size due to an increase in diffusion length, a decrease in depletion depth, or a decrease in the substrate's absorption (coefficient) and/or as the pixel's aperture decreases with respect to the pixel size. >