Four-element division algorithm
The optimization processing starts with cycling the optical phase of the first element from 0 to \(2\pi\), colored as green shown in Fig. 11a, while the target signal is measured and the phase at which the target intensity achieves maximum is recorded and set into this element, colored as red shown in Fig. 11b, before the optimization takes place at the second element. The phase of each element can be controlled by the computer. The back surface of the last scattering layer is imaged with a lens and the intensity distribution of output light can be measured by a CCD camera. The target intensity is a single-output channel selected in advance which is aimed to maximize its intensity. After the optimization, the second element is set to its optimized phase; thus, the third element is optimized with the first and second elements kept their optimized phase values, colored as red shown in Fig. 11c. The fourth element is optimized with the rest three elements setting their optimized phase values, colored as red shown in Fig. 11d. Obviously, in FEDA, the contributions of all elements are considered simultaneously. In other words, the optimization is obtained by interfering constructively from all the light fields, as shown in Fig. 11e. The optimized 2 × 2 format is called ‘father’ layer of the phase distribution. The format 2 × 2 represents the phase plane of SLM with horizontal number of elements of 2 and the vertical number of elements of 2.
Next, one element is further divided into four smaller elements with same size, as shown in Fig. 11f. Each smaller element first inherits its ‘father’s’ phase value. The process takes place for each smaller element by cycling its phase from 0 to \(2\pi\), while the signal at the focal point is monitored and the phase at which the target intensity reaches the maximum is acquired and set to replace the inherited phase from ‘father’ layer before the optimization moving to the second smaller element, colored as pink shown in Fig. 11g. The same processing is performed to the rest smaller elements, colored as green shown in Fig. 11h, i. The divisions and optimization are employed to all four elements in the ‘father’ layer in the same way. A 4 × 4 element phase array with all its elements optimized is obtained, colored as pink shown in Fig. 11j, which is called ‘son’ layer of the phase distribution. The meaning of ‘4 × 4’ is similar to the format ‘2 × 2’ described above.
The division and optimization can be continued to divided into 8 × 8 optimized phase distribution, which is called ‘grandson’ layer of the phase distribution. This procedure can continue to infinity, generating 16 × 16, 32 × 32… optimized phase masks, until the number of elements equals to the number of pixels of SLM.