![]() In the calculation process, the difference between the over-focused and under-focused intensity images is used to approximate the intensity differential, 8 – 10 meaning that the position of the in-focus image not only affects the acquisition itself but also the intensity differential, and hence, the accuracy of phase retrieval. To solve the TIE, it is usually necessary to obtain an in-focus image and the corresponding over-focused and under-focused images. Moreover, this method does not require staining 7 to obtain the phase, which can avoid direct contact and hence protect cells. This method can be used to retrieve quantitative phase information based only on measurements of the intensity distribution of the wave-field at different transmission distances, without interference or additional reference light. The non-interference phase retrieval method, based on the transport of intensity equation (TIE), 5, 6 is one of the most widely used approaches at present. However, the phase information for cells and other samples contains significant information, such as structure and optical properties, and it is therefore vital to calculate the phase based on the directly obtained intensity. Hence, regardless of whether traditional bright-field, dark-field, 4 or proportional field observation is used, only the intensity information of the samples can be observed, whereas the phase information is lost. In the field of microscopic imaging, 1 – 3 the oscillation frequency of the light wave is much higher than the response speed of the human eye or imaging device used to observe the cell structure. In a microlens array experiment, the relative error between the results from our algorithm and the actual value was only 7.1%, thus, proving the correctness and effectiveness of the proposed method. The correlation coefficient for the results of the simulation experiment reached 0.9317. Finally, the optimal in-focus image and related defocused images are used to solve for the phase of the sample using the TIE under the boundary conditions. The original image corresponding to the minimum threshold duty ratio is the optimal focus image. ![]() We first perform pixel reduction on a series of acquired intensity images, and these images are segmented using the optimal threshold to calculate the threshold duty ratios. We propose a fast phase retrieval method based on the TIE and the threshold duty ratio. The accuracy and speed of focus positioning affect the accuracy and time of phase retrieval. However, to solve the TIE, it is necessary to obtain an in-focus image. In this study, we revise AW07 to improve the intensity scaling at large magnitudes and close distances, by reconciling intensity equations with ground‐motion prediction equations.When cells are observed with a microscope, the phase information for the sample is usually obtained from the acquired intensity images using the transport of intensity equation (TIE). ![]() However, a problem with the AW07 equations is that they predict unrealistically large median intensities for large events ( M>6) at close distances. Examination of the performance of AW07 for North American earthquakes, evaluated using an extensive compiled database of DYFI observations from 2000 to 2013, suggests that there is little statistical basis for revising these equations. The intensity prediction equations of Atkinson and Wald (2007 hereafter AW07) have been remarkably successful in describing the level and intensity of motions reported under the “Did You Feel It?” (DYFI) program over the last several years. Equations that predict intensity as a function of magnitude and distance are useful tools for hazard and risk assessment, and in interpretation of both contemporary and historical earthquake information.
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