Edge spread function measurement

If you entered Imatest on this page, you may want to explore the background information in these links. Sharpness introduces sharpness measurements and MTF. Image quality factors lists the factors measured by Imatest. Table of contents documentation. Note that one cycle or line pair is equivalent to two line widths. SFR settings window. Standardized sharpening results are no longer displayed on this page because they are generally not recommended for lens and system testing Standardized sharpening was designed for comparing cameras with differing degrees of software sharpening, where RAW files were unavailable.

See Sharpening and Standardized Sharpness for details. The following results appear on the right of the plot when LSF is selected. Valuable because it does not reward extreme sharpening; it is nearly identical to MTF50 up to the onset of oversharpening, then it remains relatively constant as the sharpening peak increases above 1.

LSF correction factor for slanted-edge MTF measurements

Documentation — Current v The normalized edge profile is proportional to the light intensity. Pale brown dashed line. Left column text input settings. RMS edge roughness in pixels. A promising measurement related to image quality. Shown on the right. MTF curves and Image appearance contains several examples illustrating the correlation between MTF curves and perceived sharpness. MTF plot. Middle right image The selected Region of Interest ROIshown with the correct aspect ratio, but not necessarily the exact size.

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The following parameters are displayed below the image. ROI size in pixels ROI boundary locations Left, Right, Top, and Bottom in pixels from the upper-left corner, Edge angle in degrees, and Estimated chart contrast, derived from the average pixel levels of the light and dark areas away from the transition and gamma. May include ISO speed, aperture, and other details. Thanks to Matthias Wandel for jhead.

Key results are shown below in Bold.The LSF correction factor primarily affects very high spatial frequencies beyond most of the energy for typical high quality cameras. But it does make a difference for practical measurements: MTF50 for a typical high quality camera shown below is increased by about 1. The correction factor was turned off by default in Imatest versions 4.

It is turned on by default in versions 4. It can be set to override the default by pressing SettingsOptions III in the Imatest main window as shown belowthen checking the box for the correction. We strongly recommend turning on the LSF correction factor, i.


Note that D j is incorrect in the ISO standard. It should read. Numerical differentiation is a linear process with a transfer function that differs from ideal differentiation. The ISO formula D. This numerical difference formula may be rewritten.

The Fourier transform FT for a time or spatial shift is given in Wikipedia. For numerical differentiation, the Fourier transform is. Check or uncheck the Use LSF… checkbox as appropriate. The checkbox sets derivCorr in the [imatest] section of imatest-v2. For most applications we recommend checking the box— turning on the correction factor. To observe the effects of the LSF correction factor, we use an idealized edge, tilted 5 degrees, shown on the right.

You can click on it to download it for your own testing. The expected value of MTF at the Nyquist frequency 0.

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Here are the results without and with the LSF correction factor. Note that gamma has been set to 1 because the idealized image is not gamma-encoded. Also, the edge rotation correction that is not applied to edges slanted by less than 8 degrees.

The edge rotation is not included in the ISO standard and so is not applied to edges that fall under the ISO standard algorithm. It has the expected values of 0. Most color space files are gamma-encoded with gamma around 0. Actual gamma varies considerably, and may be complicated by a tonal response curve on top of the gamma curve.This method has particular advantages, but also has some limitations, mentioned in earlier blogs.

Another evaluation technique to characterize the MTF is based on the so-called slanted-edge method. Explained in words, this method sounds very complicated, but in reality it is really pretty simple. A very helpful strategy in understanding how this MTF measurement method works and to check the algorithms, is to run a simulation and create an artificial image with a slanted edge that is sampled by an artificial sensor e.

Such a simple simulation tool can also be used to check the influence of the various system parameters on the measurement technique.

edge spread function measurement

An example of such a simulation is shown in the following figures. First of all a synthetic image is generated that results in a slanted edged of 4 deg. A region-of-interest ROI of H x V pixels is created around the black-white transition of the slanted edge.

edge spread function measurement

This synthetic image is shown in Figure 1. Figure 1 : ROI containing the slanted edge or black-white transition. A particular column is selected in this example column number 96and all pixel values in this column are recorded to generate the SFR or Spatial Frequency Response.

The result of this operation is shown in Figure 2, with reference to the left vertical axis. Figure 2 : Spatial Frequency Response, being the values of the pixels present in column 96 of the image shown in Figure 1, and Line Spread Function, being the first derivative of the SFR.

The LSF is shown in Figure 2 as well, with reference to the right vertical axis. In this simulation example, the pixel pitch is equal to 6. Figure 3 : MTF of the simulated pixel 6. This geometrical MTF is calculated by means of the well-known sinc-function.

As can be seen, both curves coincide very nicely, indicating that the slanted edge method and the algorithms used in the calculation seem to do the job that they were developed for!

Before showing real measurements, in the next blog s a few additional improvements of the slanted edge method will be highlighted. This entry was posted on Wednesday, June 18th, at am and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2. You can leave a responseor trackback from your own site. It seems, this method can be used for area arrays only. Some applications do use linear arrays. For area arrays, this is equivalent to a simplified version of step-scanning a vertical slit.

Time scanning is replaced by space scanning because so many rows of detectors are available. This method can also be applied to linear imaging sensor also.

However, it is limited to crossline direction. I am currently trying to understand the MTF spatial frequency normalization. How does the pixel pitch correlate with the abscissa? The pixel pitch defines the sample frequency. That is becoming the spatial sample frequency.The optical transfer function OTF of an optical system such as a cameramicroscopehuman eyeor projector specifies how different spatial frequencies are handled by the system.

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It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector arrayretinascreen, or simply the next item in the optical transmission chain.

A variant, the modulation transfer function MTFneglects phase effects, but is equivalent to the OTF in many situations. Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the Fourier transform of the point spread function PSF, that is, the impulse response of the optics, the image of a point source. As a Fourier transform, the OTF is complex-valued; but it will be real-valued in the common case of a PSF that is symmetric about its center.

The image on the right shows the optical transfer functions for two different optical systems in panels a and d. The former corresponds to the ideal, diffraction-limitedimaging system with a circular pupil. Panel d shows an optical system that is out of focus. This leads to a sharp reduction in contrast compared to the diffraction-limited imaging system. This explains why the images for the out-of-focus system e,f are more blurry than those of the diffraction-limited system b,c.

Close observation of the image in panel f shows that the spoke structure is relatively sharp for the large spoke densities near the center of the spoke target. Since the optical transfer function [2] OTF is defined as the Fourier transform of the point-spread function PSFit is generally speaking a complex-valued function of spatial frequency.

The projection of a specific periodic pattern is represented by a complex number with absolute value and complex argument proportional to the relative contrast and translation of the projected projection, respectively.

Often the contrast reduction is of most interest and the translation of the pattern can be ignored. The relative contrast is given by the absolute value of the optical transfer function, a function commonly referred to as the modulation transfer function MTF.

Its values indicate how much of the object's contrast is captured in the image as a function of spatial frequency. The MTF tends to decrease with increasing spatial frequency from 1 to 0 at the diffraction limit ; however, the function is often not monotonic. On the other hand, when also the pattern translation is important, the complex argument of the optical transfer function can be depicted as a second real-valued function, commonly referred to as the phase transfer function PhTF.

The complex-valued optical transfer function can be seen as a combination of these two real-valued functions:. The impulse response of a well-focused optical system is a three-dimensional intensity distribution with a maximum at the focal plane, and could thus be measured by recording a stack of images while displacing the detector axially.

By consequence, the three-dimensional optical transfer function can be defined as the three-dimensional Fourier transform of the impulse response. Although typically only a one-dimensional, or sometimes a two-dimensional section is used, the three-dimensional optical transfer function can improve the understanding of microscopes such as the structured illumination microscope.

However, typically the contrast relative to the total amount of detected light is most important.My preferred method for measuring the spatial resolution performance of photographic equipment these days is the slanted edge method. And all of this simply from capturing the image of a black and white slanted edge, which one can actually and somewhat easily do at home. I will mainly use MTF in this article. Alas such constellations are hard to come by — but not to worry because we can make our own.

So, as better explained further down, by applying the slanted-edge method we obtain a measurement of the 2D MTF of the imaging system as setup in just one direction. Such a Modulation Transfer Function in our context represents the ability of an imaging system as a whole to transfer linear spatial resolution information i. One of the better such targets is a back-lit razor blade but in practice it can be a bridge on a satellite photo or a high quality print of a uniformly black square or rectangle onto uniformly white paper.

SFR results: Edge and MTF (Sharpness) plot

It needs to be tilted slanted ideally between 4 and 6 degrees off the vertical or horizontal and be at least 50 pixels long, or more is better. But not too long if we want to minimize the effects of lens distortion and are interested in the performance of the system in just a small spot: the resulting MTF is the localized average of the performance of the system over the length of the edge.

Even with excellent lenses spatial resolution can change significantly over the space covered by a long edge. Therefore the relative quality of the edge i. If one uses a lower quality edge, such as one printed at home, the results may be less sensitive but still have comparative value to other measurements taken with the same target.

The advantage of the slanted-edge method is that it effectively super-samples the edge by the number of pixels along it. Assuming the edge is perfectly straight not a given in some recent camera formats that rely on software to correct for poor lens distortion characteristics if it is pixels high, then the edge profile is oversampled three hundred times with great benefits in terms of effectively cancelling quantization and reducing the impact of noise and aliasing on the spatial resolution measurement.

Binning has the effect of regularizing the data while providing initial noise reduction. The physical units on the normal axis are pixels — here short for pixel pitch, which is the horizontal or vertical distance between the centers of two contiguous pixels. Since for a, say, ideally printed and illuminated edge the transition from black to white on paper is a step function centered at zero pixels below, any degradation in the ESF from this ideal can be ascribed to loss of sharpness due to the imaging system:.

If the imaging system and the edge were perfect the LSF would be an infinitely narrow vertical pulse at zero pixels a delta function — but in practice they never are so the pulse is instead spread out as shown.

Differentiation amplifies noise. The resulting curve tells us how good our equipment is at capturing all levels of detail spatial resolution from the scene.

On the other hand the curve hits the grayscale Nyquist frequency with a lot of energy still, at an MTF of around 0. The grayscale Nyquist limit refers to the maximum number of line pairs that can be represented accurately by the sensor, in this case about since the D has twice that many pixels on the short side.

With great care the method can provide absolute results but in most cases it is instead used to obtain relative results, with only one variable in the process varied at a time for example the lens. I really appreciate your time in writing this article.

It really helped my understanding. Thank you. How do you pass from the edge projected on normal many intensity values per pixel to the ESF?

The result is then regularized but tends to be a bit noisy with typical slanted edge captures. There are more sophisticated methods, however.As the X-ray imaging market keeps expanding and digital X-ray detector technology has become more important, the International Electro Technical Commission has developed an IEC standard for the device to cope with medical imaging report requirements. However, during the practical operation, we found that if the multiple pre-sampling edge spread functions ESFs were averaged directly, the MTF value would be underestimated.

edge spread function measurement

This work develops a novel method for calculating the MTF. We compared three different edge spread function ESF calculation methods. For method 1, the ESF is obtained by taking only the central line. For method 2, the ESFs are averaged directly. For method 3, the novel method proposed in this study, the ESFs would be shifted before they are averaged. We used a phantom experiment to verify the correctness of the code and confirm the results from the three methods under ideal conditions.

We measured the detector response through a homemade laboratory testing platform.

Determining the MTF of Medical Imaging Displays Using Edge Techniques

The results showed that, method 3 effectively eliminated MTF underestimation. The difference was not significant when the frequency was less than 1.

This finding suggests that to eliminate the results caused by noise without any signal processing, and to generate a smoother MTF, our proposed method can give much reliable results. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Samei, E. Intercomparison of methods for image quality characterization. Modulation transfer function. Medical Physics, 33 5— Nitrosi, A.

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Journal of Digital Imaging, 22 6 Ranger, N. Assessment of detective quantum efficiency: Intercomparison of a recently introduced international standard with prior methods 1. Radiology, 3— Medical electrical equipment—Characteristics of digital X-ray imaging devices—Part 1: Determination of the detective quantum efficiency.

Geneva: International Electrotechnical Commission.The point spread function PSF describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse responsethe PSF being the impulse response of a focused optical system. The PSF in many contexts can be thought of as the extended blob in an image that represents a single point object.

In functional terms, it is the spatial domain version of the optical transfer function of the imaging system. It is a useful concept in Fourier opticsastronomical imagingmedical imagingelectron microscopy and other imaging techniques such as 3D microscopy like in confocal laser scanning microscopy and fluorescence microscopy.

The degree of spreading blurring of the point object is a measure for the quality of an imaging system. In non-coherent imaging systems, such as fluorescent microscopestelescopes or optical microscopes, the image formation process is linear in the image intensity and described by linear system theory.

This means that when two objects A and B are imaged simultaneously, the resulting image is equal to the sum of the independently imaged objects. In other words: the imaging of A is unaffected by the imaging of B and vice versaowing to the non-interacting property of photons. In space-invariant system, i. This is known as the superposition principlevalid for linear systems. The images of the individual object-plane impulse functions are called point spread functions, reflecting the fact that a mathematical point of light in the object plane is spread out to form a finite area in the image plane in some branches of mathematics and physics, these might be referred to as Green's functions or impulse response functions.

When the object is divided into discrete point objects of varying intensity, the image is computed as a sum of the PSF of each point. As the PSF is typically determined entirely by the imaging system that is, microscope or telescopethe entire image can be described by knowing the optical properties of the system. This imaging process is usually formulated by a convolution equation. In microscope image processing and astronomyknowing the PSF of the measuring device is very important for restoring the original object with deconvolution.

For the case of laser beams, the PSF can be mathematically modeled using the concepts of Gaussian beams. The point spread function may be independent of position in the object plane, in which case it is called shift invariant.

In addition, if there is no distortion in the system, the image plane coordinates are linearly related to the object plane coordinates via the magnification M as:. If the imaging system produces an inverted image, we may simply regard the image plane coordinate axes as being reversed from the object plane axes.

With these two assumptions, i. Rewriting the object transmittance function in the form above allows us to calculate the image plane field as the superposition of the images of each of the individual impulse functions, i. Mathematically, the image is expressed as:.

edge spread function measurement

The 2D impulse function may be regarded as the limit as side dimension w tends to zero of the "square post" function, shown in the figure below. We imagine the object plane as being decomposed into square areas such as this, with each having its own associated square post function. The concept of a perfect point source object is central to the idea of PSF. However, there is no such thing in nature as a perfect mathematical point source radiator; the concept is completely non-physical and is rather a mathematical construct used to model and understand optical imaging systems.

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