A New Optical Surface Measurement Method with Iterative Sparsity-Constrained Threshold Phase Retrieval Algorithm

Algorithm 1

ITPRS.

Input: Observed intensity samplings 𝑜_𝑟, the phase mask 𝑀_𝑟.

Output: Phase of wave field 𝜑.

(1) Initialization: Using (5) to get an initial value of wave field 𝑢₀.

    𝑢^initial₀=𝑇⁻¹sqrt(𝑜_𝑟),   𝑢^𝑖₀=𝑢^initial₀.

(2) DCT threshold iteration: For the 𝑖th step

  (a) Obtain an intermediate value of 𝑢₀ using (5).

      𝑢^𝑖_𝑟=𝑇(𝑢^𝑖₀),  𝑢₀^𝑖+(1/2)=𝑇⁻¹(𝑢^𝑖_𝑟),

  (b) Update: 𝑢₀^𝑖+1=𝑢₀^𝑖+(1/2)+𝛾⋅𝑇⁻¹(sqrt(𝑜_𝑟)−abs(𝑢^𝑖_𝑟)), where 𝛾 is the weight parameter.

  (c) Solve the DCT threshold problem: DCTsoft(abs(𝑢₀^𝑖+1)), DCTsoft(angle(𝑢₀^𝑖+1)) and

  calculate the RMSE (root-mean-square error) of 𝜑=angle(𝑢₀^𝑖+1).

(3) BM3D iteration: For the 𝑗th step

  (a) Obtain an intermediate value of 𝑢₀ using (5).

      𝑢^𝑗₀=𝑢₀^𝑖+1,  𝑢^𝑗_𝑟=𝑇(𝑢^𝑗₀),  𝑢₀^𝑗+(1/2)=𝑇⁻¹(𝑢^𝑗_𝑟)

  (b) Update: 𝑢₀^𝑗+1=𝑢₀^𝑗+(1/2)+𝛾⋅𝑇⁻¹sqrt𝑜_𝑟−abs𝑢^𝑗_𝑟,

  (c) Solve the BM3D problem: BM3Dangle𝑢₀^𝑗+1 and calculate the RMSE of 𝜑=angle(𝑢₀^𝑗+1).

(4) Stop condition: In DCT threshold iteration, the condition is RMSE of 𝜑_𝑖≤𝜑_𝑖+1

   and in BM3D iteration is RMSE of 𝜑_𝑗≤𝜑_𝑗+1.