Method and Apparatus for Displaying Oct Cross Sections

Abstract

OCT cross section images of a part of a curved object are displayed by creating a series of image points and placing each image point into a corrected image in such a way that the positions of scattering points within the image coincide with or are at least closer to their real spatial distribution within the curved object.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in more detail, by way of example only, with reference to the accompanying drawings, in which:

FIG. 1 shows x,z: object space; h,v: image space; Surface Σ separates media of different refractive indices; points along the line AO are placed in the image along the line AI, corresponding to a single vertical line in the generated OCT image; S: distorted surface of OPD=constant.

FIG. 2 illustrates the acquisition of an OCT image by fan scanning the object ray.

FIG. 3 shows the distorted image of a microscope slide when scanned with a fan of rays.

FIGS. 4 a and 4b illustrate the bending images of the retina upwards to compensate for fan scanning distortion. The image in the square centred on the fovea of the normal subject is used in the processing of the RPE layer as described below.

FIG. 5 shows the evaluation of the refraction angle at the interface between the vitreous and the retina.

FIG. 6 is an exaggerated representation of the distortion of the RPE contour.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

OCT can be implemented, for example, with apparatus described in detail in our U.S. Pat. No. 5,975,697, the contents of which are incorporated herein by reference. The described processing can be carried out with a personal computer, for example, including a Pentium™ microprocessor.

Consider the case of angular OCT scanning of the retina. Since, the retina must be scanned through the pupil of the eye, fan scanning must be employed. The fan of rays converges at a point C, as illustrated in FIG. 2. A collimated beam is scanned angularly through the anterior part of the eye, where refractive elements focus it on the retina. The top part of FIG. 2 shows the fan of rays scanning the retina. The bottom part represents the image acquired by the OCT for arc circles with the center in C. Polar coordinates, r, α and a corresponding Cartesian system with axes x and z are defined for the object space with the center located in the eye pupil, C. For the image space, a simple Cartesian coordinate system (h,v) is used. The relation between a point in the object space O(r, α) and the corresponding point in the image space I(h,v) needs to be understood.

The frame grabber of the OCT system places the B-scan image in the plane (h,v), where:

h=k_hα,

v=k_vz  (2a,b)

z is the axial movement of the reference mirror from the initial position. k_h and k_v are scanning scaling factors for the transverse and axial scanner respectively. k_h is given by the number of sample pixels along the horizontal axis, 2H, divided by the maximum optical ray deflection angle, α_M. k_v is given by the number of vertical sample pixels in the image along the vertical axis V, divided by the maximum axial range, z_M covered by the axial scanner in the reference arm of the OCT interferometer.

$\begin{array}{cc}{k}_h=\frac{2H}{{\alpha }_M}k_v=\frac{V}{z_M}& \left(3a\text{,}b\right)\end{array}$

The axial scanner varies the reference path to select points within the retina, situated at a certain radial distance between r₀ and r₀+Δr. If the scanner moves by z, then the coherence gated spatial window advances from the initial position r₀ to:

$\begin{array}{cc}r=r_0+\frac{z}{n}& \left(3c\right)\end{array}$

where n is the average index of refraction of the retina, considered a constant, 1.38 everywhere in the eye for brevity.

Placing the reference for OPD=0 in the top centre of the image o and also making the object space and the image space coincide in this point, lateral and vertical errors produced by the fan scanning can be computed as:

$\begin{array}{cc}{E}^l=\left(r_0+\frac{z}{n}\right)\sin \alpha E^a=\left(r_0+\frac{z}{n}\right)\cos \alpha -r_0& \left(4a\text{,}b\right)\end{array}$

E^I measures how much the image point I moves laterally relative to the corresponding object point O, while E^a signifies how much the image point I moves axially from the corresponding object point O. For a null α angle, the errors are zero.

To better understand the distortions in the fan scanning case, let us consider a simple rectangular object, such as a microscope slide glass in FIG. 3 left. During scanning, for a certain fixed OPD in the OCT apparatus, the coherence gate selects those points from the object situated on an arc of circle with the centre in C and radius matching the reference arm length. Under these circumstances, the anterior surface Σ₁ appears in the image (FIG. 3 right) as a curved line, S₁. The same is true for the other surface, Σ₂ whose image is described by S₂. The example in FIG. 3 shows that an horizontal shape of the object surface is represented as a downward curved surface in the image space. This means that the images collected by fan scanning type have to be corrected by curving them up.

For points on the anterior surface, Σ₁, the polar coordinates in the object space are:

$\begin{array}{cc}O\left(\frac{r_0}{\cos \alpha },\mathrm{artc}\tan \frac{x}{r_0}\right)& \left(5\right)\end{array}$

In Cartesian coordinates h and v, the points of the anterior surface Σ₁ will be located in the B-scan image at points:

$\begin{array}{cc}I\left(h,v\right)=\left(k_u\mathrm{artc}\tan \frac{x}{r_0},\frac{k_vr_0}{\cos \alpha }-k_vr_0\right)& \left(6\right)\end{array}$

These equations show that the higher the angle α either side of the axis oz, the larger the vertical distortion of the image. A horizontal line in the object is represented as a downwardly curved line in the image space. Similarly, the second surface, Σ₂, given by points

$\begin{array}{cc}O\left(d+\frac{r_0}{\cos \alpha },\mathrm{artc}\tan \frac{x}{r_0}\right)& \left(7\right)\end{array}$

will be transferred to a curved line:

$\begin{array}{cc}I\left(h,v\right)=I\left(k_u\mathrm{artc}\tan \frac{x}{r_0},k_vd+\frac{k_vr_0}{\cos \alpha }-k_vr_0\right)& \left(8\right)\end{array}$

in the image plane, (h,v). The corrected image is shown in the right hand side of FIG. 4.

We inversed equations of type 6 and 8 written for each point in the image to correct T-scan based B-scan images obtained from the retina. The correction exercise is exemplified on two images shown in FIGS. 4a and 4b, that of a normal eye and of a case of neuroretinitis with optic disc edema and peripapillary serous detachment of the neurosensory retina. To correct the images, we used an average eye length of 24 mm for a normal subject, the experimental angular span of 35⁰ and an average index of refraction n=1.38 as presented in literature, as for example in E. Chen, Eye Laboratory, Ophthalmic Res., 25, (1993), 65-68 and in M. Hammer, D. Schweitzer, E. Thamm, A. Kolb, “Optical Properties of ocular fundus tissues determined by optical coherence tomography”, Opt. Commun., 186, 149-153, 2000.

It is important to associate the pathology location to the eye curvature, which is correct in the images bent upwards. For the numerical values used, the axial error is 1.2 mm and lateral error 0.44 mm. Although it is possible to estimate the eye length, for more accurate results, OCT should be first used to evaluate the eye length value, and input to the evaluations above.

Correction of the RPE and CC Layer Orientation

A second aspect of the disclosure is the correction of orientation of layers just below the foveal pit. These layers are important for correct diagnosis of eye diseases.

A B-scan OCT image of the fovea obtained with T-scanning is shown in FIG. 4a top left. Let us select a small lateral size image around the fovea as that inside the square superposed on the image. The lateral size is small and for simplicity, we choose to ignore here the distortion due to fan scanning presented previously. Due to the cumulated effect of (i) different indexes of refraction of the vitreous and of the retina and (ii) of the foveal depression, the image of the deep layers in the retina is distorted. For instance, an histological image of the fovea shows that the retinal pigment epithelium (RPE) is a straight oriented layer. However, due to the effects mentioned above, the RPE layer is slightly curved upwards. It is the scope of the present invention to evaluate quantitatively the distortion of the shape of the RPE layer and its upward deviation from a straight line. Let us consider the index of refraction of the vitreous, n_v=1.336, and of the retina up to the RPE, n_r=1.35.

The OCT image sampled by the square in FIG. 4a top left could be transferred to a calibrated chart containing orthogonal co-ordinate systems (ox to the right, oz downwards) or digitally sampled. The contours of the foveal pit can then be approximated by analytical curves:

z=ƒ(x)  (19)

In the same system of coordinates, the equation of the middle of the RPE can be approximated by:

z_p=cons tan t  (20)

The ray coming from the vitreous is incident on the retina in A_j. The equation of the refracted line A_jB_j is written for a point A_j (x_j,z_j) on the inner limiting membrane (ILM) described by equation (19), as:

x−x _j =m(z−z_j)  (21)

The slope is:

$\begin{array}{cc}m=\tan \left[\frac{\pi }{2}\pm \left({\theta }_j-\theta \right)\right]& \left(22\right)\end{array}$

The incidence angle, θ_j is

θ_j=π±γ  (23)

where γ is given by:

$\begin{array}{cc}\tan \gamma =\frac{z}{x}& \left(24\right)\end{array}$

evaluated in each point A_j.

We can calculate the coordinate of each point B_j on the RPE where the line described by the equation (21) intersects the RPE described by equation (20), and obtain the points of coordinates (x_p,z_p). If the origin of the optical path length in the vitreous is at a coordinate z=z₀ (a reference line is shown in FIG. 5), then the optical path length can be evaluated as:

v=n _v(z_j−z₀)+n_r√{square root over ((x_j−x_p)²+(z_j−z_p)²)}{square root over ((x_j−x_p)²+(z_j−z_p)²)}  (25)

This determines the shape of the RPE layer in FIG. 6. The deviation of the RPE layer from straight line is small and therefore, to illustrate the distortion, the bottom part below the broken line in FIG. 6 is represented at a vertical scale multiplied 10 times.

In points such as B_f and B_p, where the ray comes along the normal to the retina (like points in the center, A_f or outside the fovea region, A_R respectively), the x coordinates are the same and the optical path length is:

v _f =n _v(z_f−z₀)+n_r(z_p−z_f)  (26a)

or

v _R =n _v(z_R−z₀)+n_r(z_p−z_R)  (26b)

The elevation of the RPE in the center of the image can be simply calculated by subtracting equation (26a) from (26b) which gives:

δ=(n_r−n_v)(z_f−z_R)  (27)

Considering a normal average foveal pit value H=(z_f−z_R)=150 μm and the values for the indexes of refraction of the vitreous, n_v=1.336, and of the retina up to the RPE, n_r=1.35, δ=2.1 μm. Such a deviation is hard to be noticed in FIG. 5 due to the resolution, 12 μm of an SLD based OCT system. However, this deviation is comparable to the depth resolution achievable in high resolution OCT imaging of the fovea.

Claims

1. A method of creating OCT cross sectional images of the retina of an eye under examination, comprising: determining the length of the eye; scanning the retina with an OCT light beam in a fan configuration from a convergence point in the pupil to create an array of image points defined by a Cartesian coordinate system in an image space; transforming said array of image points in said image space to an array of points defined by polar coordinates from said convergence point in an object space taking into account the length of the eye and the refractive index within the eye; and displaying said array of points in the object space on a display device to provide an OCT cross sectional image of the retina.

2. A method as claimed in claim 1, wherein said refractive index is the average refractive index of the vitreous and the retina.

3. A method as claimed in claim 1, wherein the length of the eye is measured with an OCT apparatus.

4. A method as claimed in claim 1, wherein the length of the eye is estimated.

5. A method as claimed in claim 1, wherein the images are bent upwards in object space by an amount that depends on the amount of angular scanning and the value of the length of the eye so as to accurately reproduce the curvature of the object in the displayed image.

6. A method as claimed in claim 1, wherein the retinal pigment epithelium (RPE) is scanned, and said image points are transformed taking into account the foveal pit height, H, and the index of refraction of the vitreous, nv, and the average index of refraction of the fovea, nr.

7. A method as claimed in claim 6, wherein the point on the RPE in the center of the fovea is lowered by δ={nr−nv)H and all points either side are lowered by proportionally less value as the lateral distance up to an axis perpendicular on the fovea through the foveal pit.

8. A method as claimed in claim 7 wherein the foveal pit height H is evaluated using OCT and the indexes of refraction are nv=1.336, and of the retina up to the RPE, nr=1.35.

9. A method of diagnosing diseases of the fovea, wherein the state of health of the retina in the center part is evaluated as significantly depending on the amount of elevation δ={nr−nv)H of the RPE layer just below the center of the fovea.

10. A method of creating an image of the retinal pigment epithelium (RPE) of an eye, comprising scanning the retina with an OCT light beam in a fan configuration from a convergence point in the pupil to create an array of image points in an image space, and transforming said array of points into an object space taking into account the foveal pit height, H, and the index of refraction of the vitreous, nv, and the average index of refraction of the fovea, nr, and displaying said transformed points on a display device.

11. A method as claimed in claim 10, wherein during the transformation of said array of points the point on the RPE in the center of the fovea is lowered by δ={nr−nv)H and all points either side are lowered by proportionally less value as the lateral distance up to an axis perpendicular on the fovea through the foveal pit.

12. A method of generating an OCT image of the retina of an eye, comprising: scanning the retina with an incident OCT beam to create a plurality of image points in an image space, said image space bearing a predetermined relationship to said object space that introduces distortions into the OCT image due to the curvature of the eye and the refractive index within the eye; processing said image points to compensate for said distortions caused by said predetermined relationship taking into account the length of the eye, the curvature of the eye, and the refractive index within the eye; and displaying said processed image points as a true image of said surface in said object space.

13. A method as claimed in claim 12, wherein the inverse of said predetermined relationship is applied to said points in said image space to compensate for said distortions.

14. A method as claimed in claim 13, wherein said scanning is fan scanning, and said image points are processed to curve the image represented thereby to compensate for said distortions.

15. A method as claimed in claim 14, wherein said predetermined relationship is

16. A method as claimed in claim 12, wherein said OCT image is a B-scan image.

17. A method of compensating an OCT image of the retina of an eye obtained with a scanning beam passing through layers of different index of refraction, comprising: generating a plurality of image points with said scanning beam; processing said image points to compensate for the distortion introduced by said layers of different index of refraction; and displaying said processed image points as atrue image of the retina.

18. A method as claimed in claim 17, wherein processing also compensates for distortion introduced by fovial depression.