The modulation transfer function of an optical coherence tomography imaging system in turbid
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PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 56 (2011) 2855–2871
The modulation transfer function of an optical
coherence tomography imaging system in turbid
P D Woolliams1and P H Tomlins2
1Nano and Multifunctional Materials Group, National Physical Laboratory, Teddington,
TW11 0LW, UK
2Barts and The London School of Medicine and Dentistry, Queen Mary University of London,
Turner Street, London, E1 2AD, UK
Received 21 September 2010, in final form 8 February 2011
Published 8 April 2011
Online at stacks.iop.org/PMB/56/2855
In this paper we describe measurements of the contrast transfer function,
modulation transfer function and point-spread function of an optical coherence
tomography (OCT) imaging system through scattering layers having a
dimension-less scattering depth over the range 0.2–6.9.
found to be insensitive to scattering density, indicating that these measurement
parameters alone do not well characterize the practical imaging ability of an
were found to be the primary imaging limit and the effect of multiple scattering
on OCT resolution was negligible.
The results were
(Some figures in this article are in colour only in the electronic version)
Over the past two decades, low coherence interferometry has become a powerful tool for
probing biological tissue. It is noteworthy that optical coherence tomography (OCT) (Tomlins
and Wang 2005) utilizes multiple, sequential interferograms to create images of tissue
optical morphology. As this technology matures and inevitably progresses into commercial
instrumentation (Holmes 2009), a new set of scientific questions arises. In particular, the
need for accurate and meaningful instrument characterization has become important. Such
verification of parameters provided as figures of merit and can benefit the non-expert end-user
with independent verification that their instrumentation meets the expected specification.
Previous research characterized the point-spread function (PSF) of an OCT instrument
(Woolliams et al 2010) by measuring sub-resolution glass and metallic (Ralston et al 2006)
particles embedded within a clear epoxy matrix. Whilst PSF width is widely used within the
0031-9155/11/092855+17$33.00© 2011 Institute of Physics and Engineering in Medicine Printed in the UK2855
2856P D Woolliams and P H Tomlins
OCT literature as an instrument metric, a more widely accepted measure of image quality
is the modulation transfer function (MTF). The MTF describes a systems ability to spatially
resolve a sinusoidal intensity pattern with discernable contrast (Welford 1986, Gaskill 1978).
Previously, Wang et al (2007) described a method for measuring the MTF of reflectance
microscopes, with a demonstration incorporating three confocal microscopes. However, OCT
differs from reflectance microscopy modalities through its reliance upon coherence gating as
the primary mechanism for the rejection of scattered and out-of-plane light. Furthermore,
this provides the physical basis for axial resolution. OCT is widely used to image to depths
of up to a millimeter within tissues that exhibit high optical scattering. The influence of
optical scattering on OCT contrast and resolution has not been widely studied, and questions
morphology. For example, it is well known that pre-malignant epithelial changes substantially
reduce contrast in OCT images between connective and epithelial tissue types (Westphal et al
2005, Tomlins et al 2010). Such contrast is essential for conventional diagnostic analysis of
Previous investigations into the effect of scattering on OCT have been confined to the
axial dimension (Leeuwen et al 2003, Faber et al 2004). Therefore, in this paper, we present
through a series of scattering layers, each containing different densities of scattering particles.
These measurements were designed to determine how optical scattering affects the contrast
and resolving properties of a low coherence imaging system under a range of homogeneous
scattering conditions with similar bulk properties to soft human tissues.
2.1. Contrast and modulation transfer functions
The MTF of an optical imaging system characterizes how an object having a sinusoidal
reflectance profile h(x) in the spatial dimension, x, is transferred to an image. Writing such an
object function as a complex exponential we have
h(x,f) = exp(i2πfx)
where x is distance in meters and f is the target spatial frequency in line pairs per meter. The
response of an imaging system I is the convolution of its point-spread function PSF(x) with
the object h(x), i.e.
The modulation M observed in the image is characterized as a function of spatial frequency
by the expression
M(f) =I(0,f) − I(0.5f−1,f)
from which the MTF is defined as the ratio of image modulation to that of the original object,
MTF(f) = M(f)h(0,f) + h(0.5f−1,f)
It consequently follows that (Williams and Becklund 2002)
PSF(x)h(x − ξ,f)dx.
I(0,f) + I(0.5f−1,f),
h(0,f) − h(0.5f−1,f).
MTF(f) = I(0,f).
The modulation transfer function of an optical coherence tomography imaging system in turbid media 2857
Spatial Frequency (Line Pairs per mm)
Figure 1. Modulation transfer function and contrast transfer function for a Gaussian point-spread
function with an e−1radius of 5 μm.
Substitution of equation (1) into equation (2) and setting x = 0 reveals that I(0,f) takes the
form of the Fourier transform (FT) of the PSF and hence the Fourier relationship is given, i.e.
MTF(f) = FT[PSF(x)].
However, substitution of a binary reflectance object, such as a USAF-1951 tri-bar target, into
PSF with full width at half maximum (FWHM) 8.4 μm.
The curve due to the bar target will, from hereon, be referred to as the contrast transfer
function (CTF). The CTF conveys similar information to the MTF and at high spatial
frequencies the curves converge. However, over a range of low spatial frequencies 100%
modulation is maintained in the CTF, due to the binary nature of the object. The MTF exhibits
an instantaneous decrease in observed modulation because of the continuous nature of the
underlying object function.
Both curves are determined by convolution of the object function with the instrument
PSF. In OCT, the PSF in axial and lateral directions is commonly approximated by a Gaussian
intensity distribution characterized in the lateral direction by a FWHM ?x as
and in the axial direction by a FWHM ?z as
?z = 0.44λ2
The PSF in both dimensions is highly dependent upon the source central wavelength λ.
However, the lateral resolution is also dependent upon the numerical aperture NA of the
optical system, whereas the axial resolution depends upon the optical source bandwidth ?λ.
2.2. Single and multiple scattering
Due to the interferometric configuration of OCT, the detected signal i is proportional to the
2858 P D Woolliams and P H Tomlins
and negligible absorption, the OCT signal in a scattering medium decays exponentially as a
function of depth z, i.e.
?exp(−2μsz) = exp(−μsz),
where μsis the scattering coefficient of the medium and the factor of 2 accounts for the round
trip of the light within the sample. However, a sufficiently large value of μsinevitably leads
to multiple scatter. Yura (1979) defined conditions for different scattering regimes in terms of
the dimensional-less scattering parameter, d = μsz, such that when d < 1, single scattering
dominates, when d > 10 multiple scattering dominates and 1 < d < 10 describes a region
where neither single or multiple scattering can be said to dominate. Thrane et al (2000)
developed a theoretical OCT model that includes multiple scattering effects and can be used
to investigate the OCT signal for different scattering conditions. In its simplest form, ignoring
defocus, this model gives the OCT signal imsas
1 + w2
exp(−2μsz) +2exp(−μsz)[1 − exp(−μsz)]
+ [1 − exp(−μsz)]2w2
This expression is defined by the following terms:
The ratio of the probe beam e−1radii, with and without scattering, is
The lateral coherence length is
The root mean square scattering angle is
?2(1 − g).
Additional terms in equations (11)–(13) are the e−1beam intensity radius (w0) in the plane of
the sample objective lens, sample refractive index (n), focal length of the sample objective (f)
and the sample anisotropy (g).
h= 1 +
3. Materials and methods
Measurements of the lateral CTF, lateral MTF and axial MTF were obtained for a commercial
OCT microscope (EX1301, Michelson Diagnostics Ltd, UK), for which the parameters in
section 2.1 are specified as λ = 1305 nm, w0= 0.7 mm and f = 10.6 mm. The PSF
of this instrument has previously been characterized and found to yield an axial FWHM of
10.9 μm in air and a lateral FWHM of 8.4 μm (Tomlins et al 2009)in the plane of best
focus, away from which they have been shown to degrade (Woolliams et al 2010). This OCT
system consists of four semi-independent interferometer channels, with corresponding foci
each offset by a depth of 250 μm. The OCT microscope comprised a galvanometer-based
scanning system to generate two-dimensional B-Scans at a software-limited rate of 10 frames
per second. Volumetric C-scan images were obtained by translating the sample along the
lateral axis orthogonal to the B-scan image direction using a motorized linear translation stage
(Z625B, Thorlabs Ltd, UK). CTF and MTF measurements were obtained from volumetric
OCT measurements of a chrome-on-glass USAF 1951 tri-bar test chart (NT38–257, Edmund