_{1}

A new method of image processing of corona virus based on two and multiple beam interference is suggested. The method is based on measuring the fringe shift with respect to the background interference pattern. The interested application of the corona virus image in confocal microscopy is getting depth information since it has the property of optical sectioning. An accurate measurement of the fringe shift is obtained using multiple beam interference since contrast is higher than that for two beam interference. The refractive index of the corona virus image is deduced from the fringe shift. A MATLAB code is used for the processing of all images.

Corona viruses are an important family of human and veterinary pathogens that can cause enteric and respiratory infections. Corona virus infection can lead to respiratory failure, gastroenteritis, nephritis, and hepatitis.

A novel methodology of single particle image analysis is applied to select virus features in order to obtain detailed model of oligomer state and spatial relationships among viral structural proteins [

The addition of electronics, computers, and software to interferometry has enabled enormous improvements to optical metrology. Phase-shifting interferometry is used for getting data into a computer so the data can be analyzed [

In this paper, the refractive index distribution of the corona virus images is computed from the phase shift method. The corona virus fringe shift with respect to the background interference is computed to get useful information about the phase shift of the image leading map the height depth and the refractive index distribution. The results and discussions are given followed by a conclusion. The former work concerning the digital fringe shift is limited by λ/2 the inter-fringe spacing. Hence, the computation of refractive index is dependent on the fringe spacing either using two or multiple beam interference.

The complex amplitude of the corona virus as an object can be represented as follows:

where a―is the amplitude of the image, and

where a square matrix of dimensions N ´ N = 512 ´ 512 pixels (N = M) is assumed.

This work focuses on the main technique for phase evaluation of the corona virus image using the phase shifting method.

Coherent addition of a reference laser beam

Then the intensity of the two beam interference obtained in the detector plane can be expressed as the modulus square as follows:

where

Certainly, the d. c term in equation (3),

R is the amplitude of the coherent laser beam and that Y appeared in equation (3) its phase. The equation (4) is used in the fabrication of the phase-shifted images outlined in equation (5).

Since the distance between any two fringes = l/2. Consequently, according to the phase shift technique [

where the range of the interference phase _{1} is the intensity given in equation (4) at a phase_{2} has_{3} has phase

Once the phase is determined across the interference field, the corresponding height distribution h(x, y) on the surface of corona virus can be determined [

We have assumed the surface measured at normal incidence. Almost all interferometers used to measure surface height variations use phase-shifting techniques.

The refractive index of the corona virus m is computed as follows:

Since the phase of the wave cumulates traveling a distance L in a medium is

Then, the same wave that propagates over two equivalent paths L in corona virus medium and in vacuum gives the phase difference as follows (

where k = w/c = 2p/l is the propagation wave number in a medium of refractive index m while k_{0} is the propagation constant in vacuum.

By differentiation w.r.t. the path l = z, the refractive index distribution of the corona virus image is computed as follows:

Since the angular frequency is related to the wavelength as

The optical path difference represents the height variation of the image, namely

The differentiation of the height distribution

The fringe shift is

Consider the visibility expression to represent the fringe contrast as follows:

While the contrast given in case of multiple beam interference is extracted from the transmitted intensity distribution [

The parameter

It is known that the refractive index has a direct relation with the polychromatic spectral distribution of illuminating light according to the Cauchy formula as follows:

where a, and b are constants. Then the fringe shift and the refractive index are affected by the change of the wavelength.

The Corona virus image used in the processing is shown as in the ^{st} column, and at 260, 320, 380, and 440 pixels in the 2^{nd} column. The upper left plot at 10 pixels show uniform straight line fringes which is compared with the shifted fringes corresponding to the image geometry shown at the mentioned lines. Hence, we can get phase information about the image as plotted in the

Four different modulated fringes shifts are shown in the

using the cosine function to represent the phase at four different spatial frequencies at 1/32, 1/64, 1/96, and 1/128. The original image is multiplied by a factor of α = 1/32 in the interference modulated terms as follows: for a) cos (y-(1/32)A (i, j)), b) cos (2y-(1/32) A (i, j)), c) cos (3y-(1/32) A (i, j)), and d) cos (4y-(1/32) A (i, j)).

The multiple beam interferometry images of the corona virus using the Airy function to represent the phase at four different background frequencies is plotted as in the

Finally, comparing the fringe shift in the corona virus image at different frequencies f = 1/32, 1/64, 1/96, and 1/128, it is shown that the fringe shift is not resolved at frequency greater than f = 1/128.

The profile of the corona virus image taken at constant x = 150 pixels extracted from the image shown in the

Effect of mirror reflection coefficient upon the multiple beam interference images is shown as in the

The values of refractive index extracted from the

The upper cell segment selected from the image in the

Z_{ } | Z_{image } | dZ = Z − Z_{image} | µ (Z) = 1 + dZ/DZ |
---|---|---|---|

34 | 2 | 32 | 1.94 |

68 | 49 | 19 | 1.56 |

102 | 99 | 3 | 1.09 |

136 | 131 | 5 | 1.15 |

170 | 158 | 12 | 1.35 |

204 | 180 | 24 | 1.71 |

272 | 272 | 0 | 1.00 |

306 | 291 | 15 | 1.44 |

340 | 319 | 21 | 1.62 |

374 | 354 | 20 | 1.59 |

408 | 384 | 24 | 1.71 |

443 | 441 | 2 | 1.06 |

479 | 476 | 3 | 1.09 |

Z_{ } | Z_{image } | dZ = Z_{image} − Z | µ (Z) = 1 + dZ/DZ |
---|---|---|---|

51 | 63 | 12 | 1.80 |

69 | 80 | 11 | 1.73 |

84 | 96 | 12 | 1.80 |

100 | 111 | 11 | 1.73 |

118 | 126 | 8 | 1.53 |

132 | 141 | 9 | 1.60 |

149 | 152 | 3 | 1.20 |

166 | 167 | 1 | 1.07 |

Z_{ } | Z_{image } | dZ = Z_{image} − Z | µ (Z) = 1+ dZ/DZ |
---|---|---|---|

51 | 62 | 11 | 1.73 |

69 | 76 | 7 | 1.47 |

84 | 92 | 8 | 1.53 |

100 | 108 | 8 | 1.53 |

118 | 126 | 8 | 1.53 |

132 | 141 | 9 | 1.60 |

149 | 153 | 4 | 1.27 |

166 | 170 | 4 | 1.27 |

Z_{ } | Z_{image } | dZ = Z_{image} − Z | µ (Z) = 1 + dZ/DZ |
---|---|---|---|

51 | 60 | 9 | 1.60 |

69 | 75 | 6 | 1.40 |

84 | 91 | 7 | 1.47 |

100 | 107 | 7 | 1.47 |

118 | 128 | 10 | 1.67 |

132 | 144 | 12 | 1.80 |

149 | 154 | 5 | 1.33 |

166 | 171 | 5 | 1.33 |

The map of the refractive index distribution computed from equation (10) is the final object of this work.

The phase shift of corona virus images deduced from the interferometer images. The interferometer images using multiple beam interference gave better contrast than the corresponding images with the two-beam interference as expected. The effect of mirror reflection coefficient upon the multiple beam interference images discussed.

Useful information obtained from studying this virus using interferometry is extracted from the fringe shift of the modulated interference pattern namely the refractive index distribution of the whole image. Consequently, detailed and precise information about the virus may be extracted from the refractive index distribution. In addition, since the refractive index has a direct relation with the polychromatic spectral distribution of illuminating light according to the Cauchy formula it allows observe the diameter of the virus cell accurately as it changes with the wavelength of light.

Abdallah Mohamed Hamed, (2016) Image Processing of Corona Virus Using Interferometry. Optics and Photonics Journal,06,75-86. doi: 10.4236/opj.2016.65011