3 Speckle Noise Reduction and Enhancement for OCT Images
41
where λ 0 is the center wavelength of the light source, numerical aperture of the
objective is given by N A sin(α), α is half the angular optical aperture subtended
by the objective [3].
Because of using coherent illuminations, speckle noise also affects OCT in both
axial and lateral directions. Therefore, the effective resolution of OCT images, as the
smallest detectable detail, is limited by this factor [4–9]. The speckle should not be
treated as pure noise since it carries correlated information with noise [10].
3.1.1 Speckle
Speckle noise in OCT is because of multiple forward and backward scattered waves.
Multiple forward scatter occurs because of the media between the source and the
tissue to be measured. The media has a refractive index and corresponding forward
scatter causes random delay both traveling to the sample and on the return trip.
Multiple backscatter comes from material within the sample volume and material
that is close by the volume that is the focus of the measurement [9]. Speckle noise
must be accounted for either by filtering or using model based methods [11].
3.1.2 Speckle Properties
Interference of waves with random phases generates the speckle. Multiple forward
and backward scattered wavelets have random phases since scattering objects in
the sample have random depth distribution and refractive index in the sample is
fluctuating [12].
First-order statistical properties of speckle can readily be quoted if amplitudes
and phases of the individually scattered contributions are statistically independent,
and identically distributed, have phases uniformly distributed over (−π, π), and
have waves that are perfectly polarized. Then we have ‘fully developed’ speckle [13]
and the resultant phasor of the sample wave is a circular complex Gaussian random
variable. The corresponding statistics of the sample intensity is negative exponential
and the probability density function is [14]:
P I s (I s)
⎧
⎨
⎩
1
I s exp
−
I s
I s
, if I s ≥ 0
0,
otherwise
(3.3)
with moments I
n
n! I
n
.
The contrast of a speckle pattern is defined as
C
σ I s
I s
(3.4)
41
where λ 0 is the center wavelength of the light source, numerical aperture of the
objective is given by N A sin(α), α is half the angular optical aperture subtended
by the objective [3].
Because of using coherent illuminations, speckle noise also affects OCT in both
axial and lateral directions. Therefore, the effective resolution of OCT images, as the
smallest detectable detail, is limited by this factor [4–9]. The speckle should not be
treated as pure noise since it carries correlated information with noise [10].
3.1.1 Speckle
Speckle noise in OCT is because of multiple forward and backward scattered waves.
Multiple forward scatter occurs because of the media between the source and the
tissue to be measured. The media has a refractive index and corresponding forward
scatter causes random delay both traveling to the sample and on the return trip.
Multiple backscatter comes from material within the sample volume and material
that is close by the volume that is the focus of the measurement [9]. Speckle noise
must be accounted for either by filtering or using model based methods [11].
3.1.2 Speckle Properties
Interference of waves with random phases generates the speckle. Multiple forward
and backward scattered wavelets have random phases since scattering objects in
the sample have random depth distribution and refractive index in the sample is
fluctuating [12].
First-order statistical properties of speckle can readily be quoted if amplitudes
and phases of the individually scattered contributions are statistically independent,
and identically distributed, have phases uniformly distributed over (−π, π), and
have waves that are perfectly polarized. Then we have ‘fully developed’ speckle [13]
and the resultant phasor of the sample wave is a circular complex Gaussian random
variable. The corresponding statistics of the sample intensity is negative exponential
and the probability density function is [14]:
P I s (I s)
⎧
⎨
⎩
1
I s exp
−
I s
I s
, if I s ≥ 0
0,
otherwise
(3.3)
with moments I
n
n! I
n
.
The contrast of a speckle pattern is defined as
C
σ I s
I s
(3.4)