Fig. 1. (a) Example of conventional TAI for a square array designed according to Eq. (1) with a fraction parameter of $\beta =15$, and (b) its reconstructed intensity distribution at the fractional distance. (c) Phase distribution within one period of the TAI and (d) its corresponding 3D multilevel steps structure.

Fig. 2. Stemplot of the phase levels as shown in Fig. 1(c).

Fig. 3. (a) Structure of the ($m$, $n$) cell in the BP-TAI and (b) its phase configuration. The rectangular opening has a width $\mathrm{\Delta }/2$ and a height $h$, and it is shifted from the center of the cell at ($m\mathrm{\Delta }$, $n\mathrm{\Delta }$) by ${\delta }_{mn}\mathrm{\Delta }$. (c) Phase distribution within one period of the BP-TAI with $\beta =15$. (d) Comparison diagram of the phase distributions along the line through the center of the BP-TAI and the conventional TAI with $\beta =15$.

Fig. 4. (a) Experimental setup for evaluation. (b) Photo of the BP-TAI fabricated using the binary-phase distribution shown in Fig. 3(c). (c) The microscopy image of the BP-TAI. (d) Experimental results of intensity distribution at the corresponding fractional Talbot distance of the BP-TAI.

Fig. 5. Intensity distribution of the single focal spot field within one period of the BP-TAI: (a) experiment, (b) simulation, (c) ideal image. (d) Comparison of cross-sections through the intensity fields shown in (a) and (b) (note the logarithmic scale).

Fig. 6. Noise effect of the BP-TAI versus the fraction parameter.