2023-7-4 10:33:26

Polarization plays an important role in both industry and research. By using the different polarization properties, we could eliminate the highlight on the object’s surface, or detect the stress on it 1. Some polarized camera sensors are manufactured, to cater for those applications. For example, division of time(DoT), division of amplitude(DoAM), division of aperture(DoAP) and recently, division of focal plane polarimeters(DoFP)².

DoFP imaging sensors are compact and non-moving, which could capture polarized images in a snapshot. Sony IMX250MYR CMOS sensors are well-designed DoFP devices, which embed on-chip polarizers of different polarization angles for each pixel(Figure), but not on-glass polarizers, to reduce the crosstalk of polarized light.

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In clockwise, the polarizers on IMX250MYR CMOS from left bottom to right bottom pixels are $135^\circ$

Stokes vector with Stokes parameters is a set of values that describe the polarization state(Wiki). The Stokes vector $can be defined as, where is the total intensity of four polarized responses, and present the linear polarization, while presents the circular polarization state. In this case we only consider the linear polarization:$

However, this is only in the ideal occasion. In such conditions, the cross-polarized light could be completely blocked. In reality, the polarizers usually are imperfect due to manufacture. The parallel and perpendicular transmittance become $k_1$

Code Example:

def PolarInterp_Stokes(angle):
    anlge_rec = angle/180 * np.pi
    height = polar_0.shape[0]
    width = polar_0.shape[1]
    
    polar_0_vec = np.double(np.reshape(polar_0, (1, height*width)))
    polar_45_vec = np.double(np.reshape(polar_45, (1, height*width)))
    polar_90_vec = np.double(np.reshape(polar_90, (1, height*width)))
    polar_135_vec = np.double(np.reshape(polar_135, (1, height*width)))
    
    S = np.zeros((3, height*width))
    S[0, :] = (1/2)*(polar_0_vec + polar_45_vec + polar_90_vec + polar_135_vec)
    S[1, :] =  polar_0_vec - polar_90_vec
    S[2, :] = polar_45_vec - polar_135_vec
    
    M_angle = np.zeros((3, 3))
    M_angle[0, 0] = 1; 
    M_angle[0, 1] = np.cos(2*anlge_rec) 
    M_angle[0, 2] = np.sin(2*anlge_rec) 
    M_angle[1, 0] = np.cos(2*anlge_rec) 
    M_angle[1, 1] = np.cos(2*anlge_rec) * np.cos(2*anlge_rec)
    M_angle[1, 2] = np.sin(2*anlge_rec) * np.cos(2*anlge_rec)
    M_angle[2, 0] = np.sin(2*anlge_rec)
    M_angle[2, 1] = np.sin(2*anlge_rec) * np.cos(2*anlge_rec)
    M_angle[2, 2] = np.sin(2*anlge_rec) * np.sin(2*anlge_rec)
    M_angle = (1/2)*M_angle
    
    S_angle = np.double(np.matmul(M_angle, S))
    S_angle[0,:][S_angle[0,:]<0] = 0
    S_angle[0,:][S_angle[0,:]>255] = 255
    Image_angle = np.uint8(np.reshape(S_angle[0, :], (height, width)))
    return Image_angle

Result(Cross polarization, Polarization angle from 0~180):
在这里插入图片描述

References

chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://dce9ugryut4ao.cloudfront.net/LUCID-Going-Polarized-White-Paper.pdf ↩︎
Zhang J, Luo H, Hui B, et al. Image interpolation for division of focal plane polarimeters with intensity correlation[J]. Optics express, 2016, 24(18): 20799-20807. ↩︎
Qiu S, Fu Q, Wang C, et al. Linear polarization demosaicking for monochrome and colour polarization focal plane arrays[C]//Computer Graphics Forum. 2021, 40(6): 77-89. ↩︎ ↩︎

淘先锋技术网

【Stokes Vector】Stokes向量的计算以及模拟偏振的插值

Interpolating Polarization From DoFP Using Stokes Vector

References