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IEEE Photonics Journal Memory Effect Based Filter to Improve Imaging Quality
through thick scattering media. Deconvolution methods [42], [48]–[54] are exploited to demonstrate
real-time, 3D, and super resolved imaging. A point source has to be set previously to obtain its
speckle, called point spread function (PSF) [56]. Hence the deconvolution method is neither single-
shot nor non-invasively. However, the whole imaging system is well presented by the PSF, and
the deconvolution method normally turns out a high imaging quality. As a result, deconvolution
method is a good tool to analyze scattering phenomena and to explore the corresponding physical
mechanisms. For instance, the Field-Of-View (FOV) of the imaging system can be extended to
approach the memory effect (ME) range by reducing the applied pupil of the diffuser [48]. It was
further enlarged to exceed the ME range with spatial-correlation-achieved PSF [57]. A single-
shot monochromatic speckle pattern was adequate for color imaging because deconvolution still
works when the spectral overlaps existed [58]. We have recently reported the physical relationships
between the speckle patterns of different objects [59], between the PSFs at different depths of
object plane [60] and at different wavelengths [61]. Imaging with large FOV, super Depth-Of-Field
(DOF), for different objects, at different wavelength, real-time, single-shot and non-invasive has
been realized accordingly. It is obviously that better imaging quality will increase the imaging
capabilities and enlarge the application scope of the system. Phenomena or physical mechanisms
studied through deconvolution method can also be applied to speckle correlation methods and
other imaging recovery methods through scattering media.
In this paper, we present a speckle-imaging method to reconstruct incoherently illuminated ob-
jects that are hidden behind a thin scattering layer. It is the first time to analyze the noise model
of the imaging processing through scattering layer. Thus, a ME based filter is proposed for de-
convolution operation by analyzing the image degradation model. The imaging quality is improved
markedly after the ME based filter comparing to the conventional inverse filter, Wiener filter, and the
novel interferenceless method [55]. The proposed ME filter is also applied to improve the imaging
method proposed for dynamic imaging through scattering layer with a reference object [59]. The
artefact generated by the deviation of retrieved PSF can be effectively eliminated. Our method
has better consistency in restoring the center and edge of objects, and the suppression of noise
background is notable as well. The ME based filter is promising to improve the imaging quality for
other deconvolution and speckle correlation methods.
2. Experimental Principle
An imaging system, no matter how complicate its internal components are, may be lumped into a
single “black box” and be completely described by its PSF. The PSF is shift-invariant within the exit
pupil and reduces the object-image relation to a convolution equation. According to the memory
effect [62], [63], the speckle patterns from a thin scattering layer will follow the trend of incident
light when it is tilted a small angle. So if a thin scattering layer is inserted into a black box, the PSF
becomes a speckle pattern and only shift-invariant within a small range of angles (ME range) [1],
[62], [63]. By converting the angular shift invariance to lateral shift invariance, the speckle pattern
in the imaging plane is superposition of all PSFs from arbitrary point sources from the object. The
imaging process can be denoted as a correlation function as [62]–[67],
U
i
(
x
i
, y
i
) = F (x
i
, y
i
)
h
I
(x
i
, y
i
; x
o
, y
o
)U
∗
o
(x
o
, y
o
)dx
o
dy
o
(1)
Where subscripts i and o denote the image and the object plane respectively.
F (x
i
, y
i
)istheform
factor function defined as an angular correlation of the emerging speckle patterns of two incident
wavefronts with a tilted wavevector
q
a
= k
a
− k
a
′
,
F (q
a
) ∝ δ
q
a
,q
b
(
q
a
L )
2
sinh
2
(q
a
L )
(2)
The
F function has a bell shape curve of angular correlation and is more often referred to as
ME range. Imaging process through scattering layers is only valid within this range, leading to a
small FOV. However, most of the previous imaging reconstruction methods ignored the
F function by
Vol. 10, No. 5, September 2018 6901010
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