(2024) Neural etendue expander

 

What : Authors claim they made a holographic display with high étendue via neural etendue expanders that they developed, while keeping quality of images high.

 

Why : Despite expanding the display etendue is important in holographic display (for bigger, clearer images), many attempts have failed to achieve it. They had to sacrifice either FOV or display size. But to realize realistic holographic scenes, both quantities should remain large.

(etendue = FOV * display size)

 

How :

• The neural atendue expanders were realized as (neural net optimizable) diffractive optical elements(DOE).
• Optimization is done for the maximal reconstruction quality with a single SLM frame and a single expander. Both SLM patterns and the étendue expander are optimized.
• The etendue expanders magnify the size of images. In the paper, the magnification was done upto 64 times.
• What do the etendue expanders learn duting the optimization? → frequency statistics of natural images. Interesting thing is that the expanders actually ‘push’ unwanted frequencies into high frequency region.

 

• Holographic image is modeled mathematically as :

$$ I = |\mathcal{F}(\mathcal{E} \odot U(S))|^2 $$

where F : 2D Fourier transform, S : SLM modulation, U(*) is zeroth-order upsampling operator from the low-resolution SLM to the high-resolution neural étendue expander, and ⊙ is the Haramard product.

 

• Then, optimization is:

$$ min_{\mathcal{E}, S_{\{1,...,K\}}} \Sigma_{k=1}^K ||(|\mathcal{F}(\mathcal{E} \odot U(S))|^2 - T_k)*f||_2^2 $$

where Sk : the SLM wavefront modulation for the k-th target image Tk in a natural-image dataset with K training samples. f is the low-pass Butterworth filter for approximating the viewer’s retinal resolution as a frequency-cutoff functions as :

$$ f = \mathcal{F}((1+(\frac{||w||^2}{c^2})^5)^{-1}) $$

where w : the spatial frequency, c : cutoff frequency

 

• The etendue expander was produced by etching a subtrate with laser beam lithography.

 

홀로그래픽 디스플레이의 에텐듀를 고품질로 확대시키는 optical element를 개발한걸 보고한 논문.

Neural etendue expander는 Optimization으로 패턴 최적화한 뒤(Neural net 써서 앞에 neural이 붙는듯), 레이저 리소그래피로 에칭해서 만든다고 한다.  여타 지금까지 나온 에텐듀 확대 방법론들과 비교분석을 진행했고, 이게 가장 낫다는 식의 요지.