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The modulation transfer function of an optical coherence tomography imaging system in turbid

media

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IOP PUBLISHING

PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 56 (2011) 2855–2871

doi:10.1088/0031-9155/56/9/014

The modulation transfer function of an optical

coherence tomography imaging system in turbid

media

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

E-mail: p.h.tomlins@qmul.ac.uk

Received 21 September 2010, in final form 8 February 2011

Published 8 April 2011

Online at stacks.iop.org/PMB/56/2855

Abstract

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

OCTinstrument. Attenuationandincreasednoisefloorduetoopticalscattering

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)

1. Introduction

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

characterizationenablesanunbiasedcomparisonofinstruments; itprovidesquantificationand

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

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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

remainregardingtheinfluenceofscatteringontheabilityofOCTtoresolveandidentifytissue

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

malignant progression.

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

measurementsofthelateralandaxialMTFforanOCTmicroscope. Measurementsweremade

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. Theory

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)

(1)

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,

i.e.

MTF(f) = M(f)h(0,f) + h(0.5f−1,f)

It consequently follows that (Williams and Becklund 2002)

I(ξ,f) =

−∞

PSF(x)h(x − ξ,f)dx.

(2)

I(0,f) + I(0.5f−1,f),

(3)

h(0,f) − h(0.5f−1,f).

(4)

MTF(f) = I(0,f).

(5)

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The modulation transfer function of an optical coherence tomography imaging system in turbid media 2857

0 100200300

0

0.5

1

MTF

CTF

Spatial Frequency (Line Pairs per mm)

Modulation

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)].

(6)

However, substitution of a binary reflectance object, such as a USAF-1951 tri-bar target, into

equation(2), resultsinafunctionthatdiffersfromtheMTFasshowninfigure1foraGaussian

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

√2ln2

πNA

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.

?x =

λ

(7)

?λ.

(8)

2.2. Single and multiple scattering

Due to the interferometric configuration of OCT, the detected signal i is proportional to the

opticalfieldamplituderatherthanintensity. Undertheassumptionofasinglescatteringmodel

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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

s

h

i(z) ∝

(9)

ims(z) ∝

exp(−2μsz) +2exp(−μsz)[1 − exp(−μsz)]

?w2

+ [1 − exp(−μsz)]2w2

h

?w2

s.

(10)

This expression is defined by the following terms:

The ratio of the probe beam e−1radii, with and without scattering, is

?2w0

The lateral coherence length is

?

μsz πθrms

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).

w2

s

?w2

h= 1 +

ρ0(z)

?2

.

(11)

ρ0(z) =

3

λ

nf

z

(12)

θrms≈

(13)

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

OpticsLtd, UK)buriedbeneatha300μmthickscatteringlayerthatwastemporarilycontacted