This module is related method which convert to offaxis hologram.
Introduction
 Complex hologram records the amplitude and the complete phase of the diffracted optical field, reconstr uction of the complex hologram can give the 3D image of an object without the twinimage and background noise [1]. However, a conventional SLM cannot represent a complex hologram because the SLM can represent either amplitude or phase. Because a conventional amplitudeonly SLM can modulate the amplitude of an opti cal field, we can represent either the real or the imaginary part of the complex hologram with DC bias. However, when we reconstruct the 3D image of the object optically for 3D display using an amplitudeonly SLM, the reconstructed 3D image of the object is corrupted by the twinimage and background noise. On the other hand, a phaseonly SLM modulates only the phase of an optical field, and, thus, if we represent the phase of the comp lex hologram using the phaseonly SLM, the reconstructed 3D image is distorted by amplitude flattening.
 Convert complex holograms into offaxis holograms, which can reconstruct 3D images of objects without distor tion due to twin image noise, background noise, and amplitude flattening [4].
Algorithm
 In the offaxis hologram, the optical axis of the reference wave is tilted to that of the object wave. The angle between the optical axes of the reference and object waves introduces a spatial carrier within the hologram. The spatial carrier allows the separation of the desired 3D image of the object from the twinimage noise and background noise in the reconstruction stage[2,3]. To convert the complex hologram to an offaxis hologram, we multiply a spatial carrier term to complex hologram, \( H_{complex} \)
\[ H_{complex}^{spatial carrier}(x,y)= \left  H_{complex} \right  \exp \left ( j \angle H_{complex}\right ) \exp \left (j\frac{2\pi\sin\theta}{\lambda}x \right ) = \left  H \right  \exp\left[j\left( \angle H_{complex}+\frac{2\pi\sin\theta}{\lambda}x\right ) \right] \qquad \left(1\right) \]
 where \(\angle\) represents the phase of a complex function, and \(\theta\) is a tilted angle between the optical axes of the reference and object waves. Note that we need to choose the offaxis angle, \(\theta\), large enough to sepa rate the desired 3D image from the twinimage and background noise[2,3]. The spatial carrier that is added to the complex hologram separates the background noise as the zerothorder beam and the twin image as the firstorder beam, which are spatially separated from the desired 3D image in the optical reconstr uction[2,3]. To acquire an offaxis real hologram suitable for display on an amplitudeonly SLM, we extract the real part of Eq. (1) and add a DC bias to give
\[ H_{complex}^{offaxis}(x,y) =Re\left[H_{complex}^{spatialcarrier}(x,y)\right]+dc =\leftH_{complex}^{spatialcarrier}(x,y)\right\cos\left(\angle H_{complex}+\frac{2\pi\sin\theta}{\lambda} x\right)+dc \qquad \left(2\right) \]
 where dc is a DC bias added to make the offaxis hologram become a positive value.
Figure 2. Flowchart
Reference
 [1] T.C. Poon, T. Kim, G. Indebetouw, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Twinimage elimination experiments for threedimensional images in optical scanning holography,” Opt. Lett. 25, 215–217 (2000).
 [2] E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962). 16.
 [3] E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuoustone objects,” J. Opt. Soc. Am. 53, 1377–1381 (1963).
 [4] Y. S. Kim, T. Kim, T.C. Poon, and J. T. Kim, “Threedimensional display of a horizontalparallaxonly hologram,” Applied Optics Vol. 50, Issue 7, pp. B81B87 (2011)
◆ sigConvertOffaxis()
Function for Convert complex hologram to offaxis hologram.
 Parameters

angleX  Xaxis angle of offaxis 
angleY  Yaxis angle of offaxis 
 Returns
 if works well return 0 or error occurs return 1
Definition at line 1018 of file ophSig.cpp.
◆ sigConvertOffaxis_CPU()
bool ophSig::sigConvertOffaxis_CPU 
( 
Real 
angleX, 


Real 
angleY 

) 
 

protected 
Function for Convert complex hologram to offaxis hologram by using CPU.
 Parameters

angleX  Xaxis angle of offaxis 
angleY  Yaxis angle of offaxis 
 Returns
 if works well return 0 or error occurs return 1
◆ sigConvertOffaxis_GPU()
bool ophSig::sigConvertOffaxis_GPU 
( 
Real 
angleX, 


Real 
angleY 

) 
 

protected 
Function for Convert complex hologram to offaxis hologram by using GPU.
 Parameters

angleX  Xaxis angle of offaxis 
angleY  Yaxis angle of offaxis 
 Returns
 if works well return 0 or error occurs return 1