modulation transfer function中文

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Over the course of the microscope’s history, technological innovations have made the microscope easier to use and have improved the quality of the images produced. The compound microscope, which consists of at least two lenses, was invented in 1590 by Dutch spectacle-makers Zacharias and Hans Jansen. Some of the earliest microscopes were also made by a Dutchman named Antoine Van Leeuwenhoek. Leeuwenhoek’s microscopes consisted of a small glass ball set inside a metal frame. He became known for using his microscopes to observe freshwater, single-celled microorganisms that he called “animalcules.”

A microscope is an instrument that is used to magnify small objects. Some microscopes can even be used to observe an object at the cellular level, allowing scientists to see the shape of a cell, its nucleus, mitochondria, and other organelles. While the modern microscope has many parts, the most important pieces are its lenses. It is through the microscope’s lenses that the image of an object can be magnified and observed in detail. A simple light microscope manipulates how light enters the eye using a convex lens, where both sides of the lens are curved outwards. When light reflects off of an object being viewed under the microscope and passes through the lens, it bends towards the eye. This makes the object look bigger than it actually is.

Prior to diving into the experiment, the students must work out the best theoretical specifications of the studied camera lens: the MTF cut-off frequency fc and the size of the point spread function ΦAiry.

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A microscope is an instrument that can be used to observe small objects, even cells. The image of an object is magnified through at least one lens in the microscope. This lens bends light toward the eye and makes an object appear larger than it actually is.

The linear source is a practical solution to measure the MTF with light sources which would not be bright enough for use with a point source. The MTF thus measured is in 1D, orthogonally to the direction of the line. This can be proven as follows, given a source S(x, y) = δ(x).C and a lens of diameter a:

The response of the objective can be expressed as the square of the Fourier transform of the product of the source with the aperture of the lens R2(kx, ky), with (kx, ky) the spatial frequencies associated with resp. (x,y).

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An expanded beam can be focused to a narrow diffraction-limited waist, which can be necessary for use with optics or instruments that have small input apertures ...

A more in-depth quantitative analysis is then carried out using the Matlab software provided, the interface of which is shown on Figure 3.

Before making use of the camera and the analysis software, it is informative to make visual observations of the linear spread function. This allows the students to get an intuitive grasp of the aberrations, estimate the size of the LSF and for which aperture size the objective starts to be diffraction-limited.

Because the camera has a pixel size of 2.4 µm, the system (lens + camera) is thus theoretically limited by the pixel size (fc,chip = 417 mm–1 ).

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Another important point concerns the choice of the collimator and the microscope objective. It goes without saying that the two must be devoid of aberrations. Moreover, the collimator aperture must be significantly larger than that of the camera lens, and the object numerical aperture of the microscope objective must obviously be greater than the image numerical aperture of the lens not to limit the measurement.

This corresponds to the Linear Spread Function (LSF). The Fourier Transform of the LSF then gives the 1D MTF in the y-direction.

Modulation transfer function

This apparatus allows our students to measure the modulation transfer function of a camera lens with f‘= 25mm and Nmin = 0.95 which is used with a CMOS chip with 5472 × 3648 pixels and a pixel size of 2.4 µm.

Such a delicate measurement is also a good opportunity to demonstrate several key aspects of optical instrumentation, namely, the implementation of a linear source for a given optical system, the impact of the finite size of the source on the measurement, and the choice of the optical elements to image the response of the studied lens on the camera.

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SensorMTF

MTF

• Measurement apparatus: a microscope objective x40 re-images the focal spot onto a CMOS chip with 1.3 × 106 square, 5.3 µm pixels.

After a careful calibration of the magnification of the imaging of the focal spot onto the camera and tuning the exposure time to an appropriate value, the students can view the LSF (e.g. Figure 4) and the measured MTF (e.g. Figure 5) in real time. This allows them to identify the maximum aperture for which the camera lens is diffraction-limited and to quantify the effects of the different aberrations, for example the longitudinal displacement of the best focus for different aperture sizes or for different wavelengths, on- and off-axis.

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Though modern microscopes can be high-tech, microscopes have existed for centuries – this brass optical microscope dates to 1870, and was made in Munich, Germany.

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• Linear source: bright, white or coloured LED light is first diffused by a ground glass diffuser to homogenize the illumination of a thin adjustable slit which acts as a linear source

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The students are then asked to work out the sampling spatial frequency of their measurement apparatus to verify that the combination of the x40 microscope objective and the CMOS chip with 1.3 × 106 square, 5.3 µm pixels is appropriate to measure the MTF of the camera lens. A quick calculation yields a sampling frequency of about 7500 mm –1, which is clearly sufficient.

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This exercise uses the microscope equation for f(x)=x3 at x=2 that you constructed in Exercise 11b. a) What is Δx when x=2.05? What estimate does the microscope ...

The dissecting microscope provides a lower magnification than the compound microscope, but produces a three-dimensional image. This makes the dissecting microscope good for viewing objects that are larger than a few cells but too small to see in detail with the human eye. The compound microscope is typically used for observing objects at the cellular level.

Given that the focal length of the collimator is 500 mm and that of the objective is 25 mm, the magnification γ = 20. Therefore, d ≪ 30 µm in order to study the camera lens at full aperture.

We have shown an undergraduate lab setup designed to perform the measurement of the modulation transfer function in 1D of a camera lens. The use of a slit as a linear source allows to work with sources that would not be bright enough for use as a point source. Moreover, the adjustability of the slit width is educationally interesting as the students can directly see the impact of the size of the source on the LSF and subsequently on the measured MTF which they can visualize in real time thanks to a simple GUI. The aberrations of the camera lens can then be studied quantitatively in terms of the MTF. They can then identify that the objective is diffraction-limited from N = 8.

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While some older microscopes had only one lens, modern microscopes make use of multiple lenses to enlarge an image. There are two sets of lenses in both the compound microscope and the dissecting microscope (also called the stereo microscope). Both of these microscopes have an objective lens, which is closer to the object, and an eyepiece, which is the lens you look through. The eyepiece lens typically magnifies an object to appear ten times its actual size, while the magnification of the objective lens can vary. Compound microscopes can have up to four objective lenses of different magnifications, and the microscope can be adjusted to choose the magnification that best suits the viewer’s needs. The total magnification that a certain combination of lenses provides is determined by multiplying the magnifications of the eyepiece and the objective lens being used. For example, if both the eyepiece and the objective lens magnify an object ten times, the object would appear one hundred times larger.