How to model an Optical Coherence Tomography system

Optical Coherence Tomography (OCT) is a tomographic imaging system which can produce cross sectional or three-dimensional images based on light reflected or scattered from the image. This article demonstrates a design for an Optical Coherence Tomography (OCT) system and explores how OpticStudio analyses can be used to model coherence.

Authored By Kelly Farner

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Introduction

Optical Coherence Tomography (OCT) is a tomographic imaging system which can produce cross sectional or three dimensional images based on light reflected or scattered from the image. Imaging of medical tissue is the most typical application of this system since OCT is safe and high resolution; although the depth to which the light can penetrate is limited to the order of millimeters.

The OCT measurement system relies on a Michelson interferometer such that coherence between light reflected from the reference and the sample indicates that scattered light originates from a depth in the sample corresponding to the position of the reference mirror.

This article will walk through creating a model of a commercially available OCT in OpticStudio.

Model system

Cross-sectional images of the cornea and iris (A) and retinal tissue (B) of a healthy human eye are shown below. Changes in color correspond to changes in the strength of the returned light. This indicates a change in material.

 

eye cross section

 

A representative OCT system is shown below. The beam should be split evenly into two arms, one of which converges at the sample volume to minimize the area illuminated for a given scan. The source should be a collimated beam of broadband light; the large bandwidth means low coherence and high precision in locating depths which produce coherence.

 

representative system

 

Depth scans, also called axial or a-scans, measure the strength of the reflected light as a function of distance into the sample. Though it varies among types of OCT systems, depth scans are typically performed by the reference mirror such that light returned by the sample corresponds to a specific optical path difference (OPD) between the sample and the reference. Transverse, lateral, or b-scans are performed by rotating the scanning mirror in x or y, thereby translating the probe beam across the area of the sample.  

We will take our target specifications from those of commercially available OCT systems. Axial resolution, which comes entirely from source characteristics, should be on the order of 5 μm. Transverse resolution, which comes from the beam radius at the sample, should be at 15 μm. Light in the 800 nm range will be used to avoid high absorption in tissue which would limit penetration.

 

Source specifications

OCT uses interferometry in conjunction with broadband, near-IR light. Wider bandwidths give the best resolution while wavelength selection determines penetration depth in the sample material. For this example, we will use an 840 nm central wavelength, 60 nm FWHM source which provides an axial resolution of 5 μm in air via:

 

 

These spectral properties come from a commercially available superluminescent diode via Superlum possessing a common wavelength for biological imaging and a bandwidth for sufficiently high resolution. We will neglect collimating optics and begin with a source beam entering the interferometer.

OpticStudio can define broadband sources in two ways: by defining multiple system wavelengths within the appropriate range or by defining the associated coherence length as a property of the source. Coherence is the requisite source property for OCT, so we will use this method and allow OpticStudio to perform the bandwidth calculation and sampling via:

 

 

The object settings are shown:

 

non sequential component editor

 

Building the base system

In order to best model the coherence of the system and trace multiple ray paths at once, a Non-Sequential (NSC) model will be used in OpticStudio. Within the program, we must tell the raytrace and layouts to "Split NSC Rays" in order to follow all reflected and transmitted paths of an interferometer.

 

NSC Shaded Model

ray trace control

 

OCT measurements rely on interference conditions, using Michelson interferometry with broadband, low coherence light to accurately locate reflective sites within the sample. We will use free space optics, with rays split by a cube beamsplitter, a perfect reference mirror, and a model of the test object in one arm. The final system and settings are shown below in the Non-Sequential Component Editor.

 

non seq component editor

 

The beam splitter will be composed of two 45 degree prisms, which OpticStudio has built in as an object. This can be accessed by defining an object type “Polygon Object” and selecting the data file “Prism45.pob” under object properties.

 

object properties

 

To function as a beam splitter, both prisms need an ideal 50% transmission coating on the splitting surface (hypotenuse). In OpticStudio ideal coatings are defined under object properties using the term "I.50," where the number represents the per cent power transmitted at the surface.

 

splitting surface

 

Additionally, we must prevent the prisms from moving independently rather than as a cube, which would result in air gaps or surface mismatch and consequent inaccurate ray splitting. To keep the two prism objects together, object 2 should be the reference object (column 3) for object 3. This setting defines all position parameters to be measured with respect to the reference object such that any changes to object 2 will be extended to object 3.

There should be enough offset along the z-axis between the prisms and source to prevent overlap. The material for both prisms can be a standard glass (N-BK7), and the scale factor should be a positive value to adjust the prism size from its default of 2 mm. Using the reference command, the only positions to define for the second prism are Z Position (separate the prisms by the width, twice the scale factor) and x-tilt (1800).

 

polygon object

 

Building the sample arm

After the beam splitter, one path for the rays must encounter a scanning mirror, focusing lens, and a sample model. For this example, we will let the rays in the z-direction be the reference arm and in y be the sample path. Object 4 will perform the lateral scan using a Rectangle object with material MIRROR. Coordinates (0, 20, 20) put the mirror slightly above the center of the beam splitter; an x-tilt of 45o will be the zero point of a lateral scan, and changing this tilt performs the scan. The x and y half widths should be large enough to catch the whole beam, 7.5 mm.

 

building sample arm

 

Object 5 will be a focusing lens. The spot size at the sample determines lateral resolution, so we will begin with a simple plano-convex lens of about 50 mm EFL and rely on optimization to find the best settings later. Non-Sequential mode defines lenses as a single object of type “Standard Lens.” Coordinates (0, 20, 40) keeps the lens level with the scanning mirror and 20 mm away (this distance is arbitrary in collimated space). For simplicity we will use N-BK7. Parameters 1 through 9 define the power of the lens: Radius 1 will be the curved surface, +25 mm, Conic 1 and 2 will be zero for spherical lenses, Clear and Edge 1 and 2 will all set a 10 mm radius, Thickness can be set initially at 5 mm, and Radius 2 will be the planar surface, which in NSC is defined by a radius of 0.

The sample, object 6, will begin with the simplest model option, a single reflective surface from which there will either be coherent reflection or not. A Detector Rectangle of material MIRROR provides reflectivity while allowing us to observe the beam at the sample. The sample should be in line with the focusing lens and approximately 50 mm away (best focus will be found through optimization). With an anticipated spot size (transverse resolution) about 15 μm, half widths of 0.05 mm and 100 pixels in both x and y will allow us to resolve the spot.

 

Reference Arm

This portion needs only a planar reference mirror, object 7, which can be adjusted in z to change the path difference (depth scanning). It will again use a Detector Rectangle of material MIRROR, for the reasons above, which should be in line with the source and beam splitter. A pickup solve for z-position from the sample object with a 20 mm offset accounts for the y portion of the sample arm; the actual OPD 0 position needs to be found based on the system. Half widths of 7.5 mm and 100 pixels in each direction provide sufficient detector capabilities.



reference arm

 

Output Collection

Non-Sequential mode automatically traces the rays from the sample and reference surfaces back to the beam splitter when those surfaces are defined as mirrors. This automatic recombination is the primary benefit over Sequential mode, which would require manual definition to retrace these paths.

A diverging lens is needed to view Michelson fringes. This will be a Standard Lens of N-BK7 collecting the recombined rays (below the beam splitter in negative y space). Coordinates (0, -20, 20) center it opposite the scanning mirror. Lens parameters will follow from the focusing lens with the exception of -20 mm Radius 1 and 1 mm thickness.

 

diverging lens

 

Object 9 will be a Detector Rectangle directly below the lens. Coordinates should be (0, -30, 20), and a 90 x-tilt makes the surface orthogonal to beam propagation. Half widths of 7 mm and pixel settings of 100 will suffice for simulations.

 

Optimization

The main specification to be optimized is focused spot size at the sample. The relevant merit function needs two initializing operands: NSDD with all parameters as zero clears the detectors of previous data, and NSTR with all parameters as one defines the ray trace. The spot size operand is NSDD, where the pixel number identifies which value is measured (Pix#=-9 for RMS Radius); the target value is 0 to find the best focus, and weight should be nonzero. An operand must be defined to ensure rays reach the detector; a detector with no rays also returns a zero spot size. NSDD with Pix#=-3 pulls number of rays, and leaving the weight as zero and defining a weighted greater-than operand (OPGT) with a target to ensure a non-trivial number of rays meets this requirement.

 

optimization

 

The focusing lens parameters of object 4 (radii and thickness) and the detector position should be set as variables in order to find the best spot size. One result of optimization gives an RMS radius of 10 μm. The focal length did not change significantly, approximately 48.8 mm, and the sample moves to 90.113 mm in the z-axis. Shown below are the lens parameters after optimization, along with the spot size before (left) and after (right).

 

optimization (after)

 

OCT simulation

Time Domain Depth

Depth scanning in the time domain is based on the coherence gate and scanning reference mirror, such that the two paths only interfere if the optical path difference OPD is within the coherence length. This is the reason we use a broadband source with low coherence, as a short coherence length lets us most accurately predict where in the sample interfering light originates for a given reference position. Images of the sample are recreated pixel by pixel using the strength of the reflected light; the coherence gate serves only as a means of identifying the position of a reflection site within the sample.

We will start with a coherence length of 20 mm, as this gives us a larger margin of error so as to find the correct reference position, and decrease to our source coherence length having found the approximate mirror position. Additionally, we will begin by using a single surface to represent the sample. This is analogous to a single re-emitting point in a sample and means that the reference mirror will only change the path length. We can use multiple mirrors to model a sample volume and observe how adjusting the reference mirror changes the target point in the sample in order to remain within the coherence length.

The degree of interference between the two paths will be analyzed using the Coherent Irradiance of the detector viewer. This option is accessed under the drop-down properties option of the detector viewer where the previous viewers have used Incoherent Irradiance. Ray traces under this setting keep track of phase of each ray to add the complex parts separately.

 

detector viewer: output

 

Sufficient analysis rays must be used to clearly discern an interference pattern. For a 20 mm coherence length we need at least a few million rays, and the first examples use 15 million; lower coherence lengths require significantly more rays. With the sample positioned at 90.113 mm in z, experimental ray traces show that interference only occurs for reference mirror positions less than 125.113 mm. Knowing that the coherence length is 20 mm, the upper reference limit should be 10 mm from the lower limit; experimentally we can see that interference fringes disappear beyond 115.113 reference mirror position. Positioning the reference mirror between these limits produces strong fringes with each ray trace. Shown below are ray trace results for the center and limits of the coherent result.

 

ray trace results

 

This lets us find the nominal OPD=0 position, 121.113 mm, at the midpoint between our approximate limits. Decreasing the coherence length until we reach the 12 μm of our source gives progressively more precision in locating the reflection site, as the range of reference mirror positions which are within the coherent gate will decrease. Shown below is the interference pattern for a 5 mm focal length, which now requires 80 million rays in order to see interference.

 

interference pattern

 

Swept Source Depth

The current system can be altered to work in the Fourier domain. A spectrometer or a swept source wavelength can be used to view the OPD effect on spectral modulation; while the former requires additional design work, the latter can be simulated with simple changes to the source parameters. By returning the coherence length to zero and defining a monochromatic wavelength, we can sweep a narrowband source through the same range. Modulation will be observed in the peak coherent irradiance as a function of wavelength, and the period of oscillation is related to the path difference between the reference mirror and reflective sites within the sample. By modeling our sample as a single surface, we will see only one modulation frequency, but a volumetric sample would superimpose the periods of each path difference for each reflecting site. A fourier transform of the oscillating signal provides a line scan of signal strength as a function of position, with peaks in this function corresponding to strongly reflective points in the sample.

Swept source (SS-OCT) uses a fixed reference mirror and determines path differences based on the degree of modulation in the spectral output. For our sample surface this means that a wavelength scan at one reference position contains information only on one path difference; for a volume sample, each re-emitting point in the sample would contribute its OPD signal to the output. As before, a single mirror surface should represent the sample such that we detect the spectral oscillation from one path difference rather than many corresponding to a volumetric re-emitter, and for high resolution it is necessary to use sufficiently small wavelength steps. 

To observe this effect in OpticStudio, we set the reference mirror to a position corresponding to a small path difference (124.113 mm in z) and adjust the wavelength to observe oscillation. Repeating with a larger OPD (reference mirror at 125.113 mm in z) should result in a faster oscillation. Shown below is an observable change in coherent power at an OPD of about 2 mm.

 

observable change

 

KA-01600

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