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Camera MTF

jems offers a simple procedure to measure the Modulation Transfer Function (MTF) of the image acquisition system (CCD or film). The procedure is based on the Fourier analysis of the noise of the acquisition system (under uniform illumination). The Point Spread Function (PSF) is finally calculated using the fitted MTF parameters. The PSF is the kernel used to convolve the simulated HRTEM images in order to introduce the MTF of the camera.

Figure1

Figure 1 Camera MTF frame ( rotational average, MTF, goodness of fit).

Figure 1 shows the MTF frame, the MTF approximated by a non-linear fitting procedure using the micrographs listed in the table. The ++ loads series of experimental micrographs and starts the fitting procedure. The elements of the series (of same size and type) must be named "name_0000", "name_0001", ... , "name_i", ... where "name" is any character string(not containing) "_" and 0000, 0001, 0002,..., i, ... are consecutive sequence numbers. The fitting procedure can also be started at any micrograph of the suite (select "image_i"). Button Start restarts the fitting procedure.

The 2 orange lines select the range of the experimental data used by the fitting procedure.

Figure 2 shows the dialogue that loads the first noise image (raw format) of the series. The noise images were acquired using a CM-20 microscope and a Gatan 1024 x 1024 pixels (24 μm pixel size).

Figure2

Figure 2 Dialogue to load raw images (Digital Micrograph).

The MTF is evaluated by taking the difference of 2 images in order to eliminate the non-uniformity of the image background and then by performing a Fast Fourier Transform (FFT) followed by a rotational average of the power spectrum. The rotational average is fitted to gaussian, lorentzian (or a combination of) functions to produce the MTF and the PSF of the camera. The fitting procedure automatically starts when the series of noise images is loaded. It can also be started at any micrograph of the series (select "image_i") or restarted on the whole series using the Start button.

It is important to note that the MTF is slightly overestimated using this fitting procedure and the PSF is narrower than the effective camera PSF. As a result, simulated images do have a slightly better resolution than experimental images.


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Levenberg-Marquardt

The Levenberg-Marquardt default fitting parameters can be modified (Fig. 3). The proposed set of parameters is usually adapted. The fitting parameters can be exported to Mathematica as a notebook and the goodness of the fit displayed at the bottom of the plot (Fig. 1). The fitted MTF and the associated Point Spread Function (PSF) are show in Fig. 4.

Delta Lambda

Figure 3 Levenberg-Marquardt fitting parameters.

MTF PSF

Figure 4 MTF and PSF of Gatan CCD camera 1024 x 1024 pixels.


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Cameras

The fitted MTF and PSF functions can be added to the list of cameras MTF (Fig. 5) and saved in the default jems folder (~/jems or ~/jemsV5). At start time jems automatically reads the liste and make them available for HRTEM image simulation. The PSF of the camera at the CameraMTF of the table is a Dirac Function δ(0). and the MTF is a uniform function u(x) = 1.

MTF

Figure 5 Cameras

The tool buttons attached to the table allows to: