The goal of the paper is to simplify a simulation of cascaded Fresnel diffraction (CFD) by reducing the number of integrals and giving a solution for arbitrary plane. The simplification becomes possible with a use of CFD theorem. CFD theorem is formulated and proved. CFD theorem for simplification of one-lens model and two-lens model is demonstrated, and their mathematical models are obtained. As a result, the number of integrals describing diffraction and light propagation in lens models is decreased multiple times. We consider the optical field in any plane, making our approach more universal by assuming ideal point spread function. This approach may be applicable to numerical simulations as well as analytical investigations, optimizations, and designs. Our work benefits Fresnel diffraction method for modeling complex optical systems.
Capacitive touch sensor screen with the metal materials has recently become qualified for substitution of ITO; however several obstacles still have to be solved. One of the most important issues is moiré phenomenon. The visibility problem of the metal-mesh, in touch sensor module (TSM) is numerically considered in this paper. Based on human eye contract sensitivity function (CSF), moiré pattern of TSM electrode mesh structure is simulated with MATLAB software for 8 inch screen display in oblique view. Standard deviation of the generated moiré by the superposition of electrode mesh and screen image is calculated to find the optimal parameters which provide the minimum moiré visibility. To create the screen pixel array and mesh electrode, rectangular function is used. The filtered image, in frequency domain, is obtained by multiplication of Fourier transform of the finite mesh pattern (product of screen pixel and mesh electrode) with the calculated CSF function for three different observer distances (L=200, 300 and 400 mm). It is observed that the discrepancy between analytical and numerical results is less than 0.6% for 400 mm viewer distance. Moreover, in the case of oblique view due to considering the thickness of the finite film between mesh electrodes and screen, different points of minimum standard deviation of moiré pattern are predicted compared to normal view.
Diffractive spatial optical modulators (SOM) employing a fine-pitch pixel array were introduced. The micromechanical designs of the lead zirconate titanate (PZT) actuator and mirror ribbon structure were optimized for a small volume while maintaining the same level of performance. The same design rule and fabrication equipment were used for a new 10-µm-pitch and conventional 16-µm-pitch SOM. The optical efficiency of the new SOM was 78% (zeroth-order diffraction), which is an improvement over that of the 16-µm-pitch SOM (73%). The full on/off contrast ratio showed no differences, and a high displacement of 500 nm was achieved. The stress of the Pt/PZT/Pt actuating layer was the main parameter affecting the initial gap height and displacement of the ribbon. The required ribbon flatness could be achieved by applying a stress gradient on the SiN layer. The temperature-sensitive characteristics, which degrade image quality, could be minimized by a mechanical compensation method that takes advantage of the thermal expansion effect of Si substrates. The estimated lifetime of the device is >4000 h. The developed fine-pitch SOM device has sufficient response time and ribbon displacement to be suitable for high-quality embedded laser-projection displays. The VGA optical module was successfully demonstrated in a mobile laser projection display.
Diffractive spatial optical modulators (SOM) with fine pitch pixel array were introduced for the mobile applications of
laser projection display which requires the small volume, low power consumption and high optical efficiency.
Micromechanical designs of piezoelectric (PZT) actuator and mirror ribbon structure were optimized for small volume,
but keeping the same level of the other performance. Even though the same design rule and fabrication equipment were
used for 10 um pitch SOM and 16 um pitch SOM, the optical efficiency of the fine pitch SOM was 78 % for the 0th order
diffraction and is better than that of 16 um pitch SOM (73%). The full on/off contrast ratio has no difference between 10
um pitch and 16 um pitch SOM. All the optical characteristics coincide well with the theoretical estimations. High
displacement of 500nm, which is enough to modulate the three Red, Green and Blue colors were achieved by the control
of the thicknesses and stresses of constituent structural layers. It was found that the stress of Pt/PZT/Pt actuating layer
was the main parameter affecting the initial gap height of the ribbon and also its displacement. For improving the optical
properties of the SOM devices, the required ribbon-flatness could be achieved by applying a stress gradient on the SiN
layer to compensate for the stress unbalance between Al mirror and SiN supprting layer. The temperature sensitive
characteristics of the SOM device, which degrades the image quality, could be minimized by a mechanical compensation
method using a thermal expansion effect of Si substrates. This concept could be applied in most of the bridge type
MEMS structure. The most critical parameter which limit the SOM device lifetime was found to be the ribbon
displacement degradation. By using a temperature accelerating lifetime measurement method based on the displacement
degradation the estimated lifetime was more than 4,000 hrs and is of acceptable level in the mobile application. In short,
the developed fine pitch SOM device, for making small volume of optical module, has sufficient response time and
ribbon displacement for modulating the red, blue and green colors with one SOM chip and is suitable for high quality
embedded laser projection displays. Optical module with VGA is successfully demonstrated for its potential applications
in mobile laser projection display such as a embed projection cellular phone.
A diffractive optical modulator has been fabricated based on a micromachining process. Novel
properties of its fast response time and dynamics were fully understood and demonstrated for the
strong potentials in embedded mobile laser display. Bridged thin film piezo-actuators with so called
open mirror diffraction structure has been designed. Optical level package also was achieved to
successfully prove its display application qualities. Display circuits and driving logic were developed
to finally confirm the single-panel laser display at a 240Hz VGA (640×480). With its efficiency of
more than 75% and 13cc volume optical engine with the MEMS-based VGA resolution SOM
showed 7 lm brightness at a 1.5W electrical power consumption. Detailed design principle,
fabrication, packaging and performances of the invented SOM are described.
A new type of diffractive spatial optical modulators, named SOM, has been developed by Samsung Electro-Mechanics
for laser projection display. It exhibit inherent advantages of fast response time and high-performance light modulation,
suitable for high quality embedded laser projection displays. The calculated efficiency and contrast ratio are 75 % and
800:1 respectively in case of 0<sup>th</sup> order, 67 % and 1000:1 respectively in case of ±1st order. The response time is as fast as
0.7 &mgr;s. Also we get the displacement of 400 nm enough to display full color with single panel in VGA format, as being
10 V driven. Optical module with VGA was successfully demonstrated for its potential applications in mobile laser
projection display such as cellular phone, digital still camera and note PC product. Electrical power consumption is less
than 2 W, volume is less than 13 cc. Brightness is enough to watch TV and movie in the open air, being variable up to 6
lm. Even if it's optimal diagonal image size is 10 inch, image quality does not deteriorate in the range of 5 to 50 inch
because of the merit of focus-free. Due to 100 % fill factor, the image is seamless so as to be unpleasant to see the every
pixel's partition. High speed of response time can make full color display with 24-bit gray scale and cause no scan line
artifact, better than any other devices.