Supplementary Materials
Supplementary Table 1 Summary table defining the notations used in the equations

The center wavelength of the source
k  2  The center wave number of the source
The value of the light intensity at any point in the image
It
The background intensity
Ib
C image
The image contrast
Ir
Is
Intensity of the reference beam at the detector
Intensity of the sample beams at the detector
I inc
The incoherent light intensity which consists of the intensities of light reflected and
backscattered from different depths in the sample and from unwanted
reflections in the optical system itself
r 
 rs r , z ,  The real part of the complex degree of the correlation between the sample light
field amplitude backscattered from within the sample at the depth of z and
the reference light field amplitude reflected from the reference mirror
U s r , z; t    The sample light field amplitude backscattered from within the sample at the
depth of z
U r r, t  The reference light field amplitude reflected from the reference mirror
  kNA2
NA  nm sin  0 The numerical aperture of the objective lens
0
0
A constant phase difference between two arms from other optical components
The maximum ray angle that can be collected by the objective,
nm
The refractive index of the immersion medium between the objective lens and the
sample such as the water
R 
The spectrum response function of the detector
The illumination intensity distribution in the pupil plane of the objective
U  
The angle that each ray makes with the z axis,

The defocus z in the sample arm
z
G 
The power spectrum of the source
Ln
Lommel’s function
The lateral displacement between the focuses of the reference and object beams in
r
the image plane,

 d o, i
The differential scattering cross section

f o, i
The scattering amplitude
b
The backscattering cross section

 
ks  k i  o

ks  ks  2k sin  2


The angle betweenthe direction of the incident plane wave i and and the direction

of the scattered field in the direction o
 
 



 n k s 
Cn rd 

rd  rd
L0
The angle between the polarization of the incident light field and the direction of

the observation o
The spectral density
Thecorrelation function of the refractive index of the sample
The magnitude of the distance between two points in the medium
The cutoff correlation length
ns21
The variance of the refractive index fluctuation
ns
The average refractive index
ns1
ns

m
D
z
R
G 
R 
I0
s
Ns
s
 s di 
The fluctuation of refractive index, also known as the normalized refractive index
fluctuation

The refractive index at any point r within illuminated volume in tissue
The Gamma function
A parameter describing fractal behavior of fluctuations of tissue refractive index
A typical dimension of the coherent probe volume element such as its largest
length
The depth of the coherent probe volume element beneath the tissue surface
The power reflectivity of the reference mirror
The spectrum of the light source
Thge rsponse function of the detector.
The incident intensity at the tissue surface
Thescattering coefficient
Number density of particles in the coherence volume
The scattering cross-section.
The optical cross section of an individual particle with diameter di and volume
i
g
The number of particle diameters.
The reduced scattering coefficient
The anisotropy factor defined as the average value of the cosine of the scattering
 rst
The degree of the temporal coherence

ng
zN
the degree of the spatial coherence
M
 s
s
rs
zA
0
NA
dis
rs
angle cos 
The group refractive index
the nominal focus position, i.e., the location of focus without refractive index
mismatch
The actual focus depth in the sample
The total optical path of the light in one arm of the interferometer when the focus
is at the surface of the tissue
The additional optical path of the marginal rays in the present of the refractive
index mismatch in the sample arm
The additional phase in the sample arm induced by the dispersion effect
The 1/e irradiance radii at the depth z within tissue
r0   f kw0 
w0
0 z 
f
 rms
z f
The 1/e irradiance radius at the depth z in the absence of scattering
The 1/e intensity radius of the incident beam in the lens plane
The lateral coherence length of a spherical wave in the lens plane due to a point
source located at the depth z
The focal length of the objective lens
The rms scattering angle of tissue
The focal depth of the microscopic objectiv
Supplementary description of the FFOCT system specifications
The en face images were obtained by a FFOCT system recently developed in our Lab. The
details of the setup were reported elsewhere ( Zhu et al. 2015a). Briefly, the system is based
on a Linnik interference microscope illuminated by a customized Köhler illuminator in which
the light source is a 20-W tungsten halogen lamp with a center wavelength of 550 nm and a
bandwidth of 200 nm. The identical microscope objectives (20x, 0.5 NA, Olympus ) are used
in both the reference and sample arms. The interfermetric images are projected onto the
surface of a CCD camera array (Matrox Iris GT300，pixels, 640480; pixel size, 7.4 m7.4
m, working at a maximum rate of 110 frames/s) by use of a lens of focal length 260 mm.
The reference surface is a polished surface of a YAG (Y3AL5O12) crystal rod with a
reflectivity of 8%. The rod is attached to a piezoelectric stage actuator (PZT) (Model
AE0505D16F from Thorlabs ). The measured resolution of the system in the lateral and depth
directions are 0.89 m and 1.3 m, respectively, larger than the corresponding theoretical
predictions of 0.5 m and 0.7 m. We attribute the difference between theory and experiment
to the large optical aberrations.