**4.5 Object detection**

In this section we demonstrate that object detection is another example of objects analysis that can be realized by the examination of Fraunhofer diffraction patterns obtained by DHM.

The hologram of a microscopic character with the shape of a zero '0', figure 23a, is used to calculate the phase image shown in figure 23b.

Fig. 23. Hologram of a microscopic character with zero shape (a), scale bar: *50 m*. Phase image reconstruction (b)

The microscopic character with zero shape will be detected when mixed with other microscopic characters. Figure 24 shows two holograms and the respective phase image reconstructions corresponding to microscopic characters with two different shapes: twenty '20' (A) and ten '10' (B). Here besides the microscopic character other elements exist to complicate the detection process.

Fig. 24. Holograms, scale bar: *50 m* (left) and phase image reconstruction (right) corresponding to microscopic characters with two different shapes: twenty '20' (A) and ten '10' (B).

In this section we demonstrate that object detection is another example of objects analysis that can be realized by the examination of Fraunhofer diffraction patterns obtained by

The hologram of a microscopic character with the shape of a zero '0', figure 23a, is used to

**4.5 Object detection** 

image reconstruction (b)

A

B

'10' (B).

Fig. 24. Holograms, scale bar: *50* 

*m* (left) and phase image reconstruction (right)

corresponding to microscopic characters with two different shapes: twenty '20' (A) and ten

complicate the detection process.

calculate the phase image shown in figure 23b.

(a) (b)

Fig. 23. Hologram of a microscopic character with zero shape (a), scale bar: *50* 

The microscopic character with zero shape will be detected when mixed with other microscopic characters. Figure 24 shows two holograms and the respective phase image reconstructions corresponding to microscopic characters with two different shapes: twenty '20' (A) and ten '10' (B). Here besides the microscopic character other elements exist to

*m*. Phase

DHM.

The hologram of a microscopic character with zero shape, figure 23a, is used to calculate the Fraunhofer diffraction pattern shown in figure 25a. The radial intensity curve *IR(u)* and the corresponding frequency spectrum are shown in figure 25b.

Fig. 25. Fraunhofer diffraction pattern of the microscopic character with zero shape (a) and the radial intensity curve (b)-upper and the corresponding frequency spectrum (b) lower.

According to figure 25a, the Fraunhofer diffraction pattern consists of elliptically shaped fringes with similar forms to that of the zero character. The fringes' width variation along their perimeter is detected by the radial intensity curve and with the subsequent spectral analysis the largest and smallest radius of the zero character can be obtained. The two peaks are signaled with arrows in the spectrum, figure 25b-down. They are positioned at the spatial frequencies *7.12 mm-1* and *11.10 mm-1*, that represent the biggest and smallest radius of the zero character respectively. According to the peaks' spatial frequencies, the largest and the smallest radii are *140 μm* and *90 μm* respectively.

For object detection the holograms of a microscopic characters with '20' and '10' shapes, figure 24 (left), were used to calculate the Fraunhofer diffraction patterns shown in figure 26 (left). The radial intensity curve *IR(u)* and the corresponding frequency spectrum is shown in figure 26 (right).

In the frequency spectrum shown in figure 26 (right) appear, mixed with other peaks, two peaks at the same spatial frequency as those that are characteristic of the zero shape frequency spectrum. In this way, the object detection can be generalized for other objects with irregular forms, because the spectrum of the radial curve of the object's diffraction pattern presents a sequence of peaks that characterize the form of the object. A unique spectrum is associated with each form.

As has been shown, this method of object detection is similar to the qualitative analysis in xray diffraction, i.e. the presence of an object is characterized by the presence of peaks in appropriate positions in the spectrum. This analogy is very important because all the developed tools for the qualitative analysis in x-rays can be used for object detection.

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**6. Acknowledgment** 

**7. References** 

Fig. 26. Fraunhofer diffraction patterns of corresponding hologram of figure 24 (left) and the radial intensity curve with the corresponding frequency spectrum (right).
