Digital Holography - Distance Meter

Holography

Grating製作與原理

sensitive to energy（exposure）= intensity * time = |Uo(x,y)|^2 * t = |a(x,y)|^2

z0 = film

object wave Uo(x,y) = |a(x,y)|*e^j fi(x,y)

reference wave Ur(x,y) = |A(x,y)|*e^j fi(x,y)

Exposure E(x,y) = I(x,y)*t = |Uo(x,y) + Ur(x,y)|^2 * t

tA(x) = BetaE^(x)

= Beta * t * I(x) 

= Beta * t * |A|^2 + Beta*t{|a(x)|^2 + A_star(x)a(x) + A(x)a_star(x)}

=t_beta + Beta’*{|a(x)|^2 + a|A||a(x) [fi_r-fi_o]|}

當重建時的調變元素

Reconstruct of object wave Illumination wave Up(x)照Hologram film重建，穿過去的光

Transmitted wave Ut(x)

= Up(x)*tA(x)

= Up(x)*t{|a(x)|^2 + A_star(x)a(x) + A(x)a_star(x)}

= A(x)*{t_beta + beta’*[|a(x)|^2 + A_star(x)a(x) + A(x)a_star(x)]}

= U1(x)+U2(x)+U3(x)+U4(x)

{

U1(x) = A(x)*t_beta = directing transmitted A(x)

U2(x) = beta’*|a(x)|^2*A(x) = Modulated A(x)

U3(x) = beta’*|A|^2*a(x) = original object wave（primary image，virtual image）

U4(x) = beta’*|A|^2*e^j fi_r(x,y)*a(x)^x = conjugate image，real image

}

由不同角度的共軛光去重建

U4(x) = beta’*|A|^2*a(x)^x，conjugate image a(x)^2 real image會出現在virtual image方向，real image看起來會跟virtual image相反，例如凹凸前後相反看起來不合日常邏輯。

Fourier Transform 待補

Fresnel Equation 待補

由三角原理求距離

其中在此範例 theta i = 0，grating light pair = 1/125*1/2mm，波長 = 532nm，CCD Pixel size = 1.75um，theta A = 4.5mm = 雷射通過光圈，O0~O1|O-1 = 中間強度干涉分佈最強與旁邊兩點的距離任取一。