GB2499435A

GB2499435A - Production and analysis of depth-resolved electromagnetic signals

Info

Publication number: GB2499435A
Application number: GB1202751.2A
Authority: GB
Inventors: Stephen J Matcher
Original assignee: University of Sheffield
Current assignee: University of Sheffield
Priority date: 2012-02-17
Filing date: 2012-02-17
Publication date: 2013-08-21
Also published as: GB201202751D0

Abstract

Obtaining and analysing a depth-resolved signal along an electromagnetic radiation path comprises using a delivery section arranged to emit polarised electromagnetic radiation and a calibration section 170 comprising at least three reference surfaces 171a, 171b, 172a, 172b arranged in a path of the radiation emitted by the delivery section. A signal associated with a sample 150, also in the radiation path, and the calibration section is detected at a polarisation sensitive radiation detection section. Based on the received data, at least one of an absolute orientation of a fast-axis of the sample, a completely specified Jones matrix for the sample, or a completely specified Jones matrix for the electromagnetic radiation path between the calibration section and the detection section, is determined. The reference surfaces may be the faces of retarders such as quarter wave plates 171, 172 and form part of a polarisation-sensitive optical coherence tomography (PS-OCT) device or similar interferometer device.

Description

1

Production and Analysis of Depth-Resolved Electromagnetic Signals

[0001] This invention relates to production and analysis of depth-resolved signals, and in particular those involving polarized electromagnetic radiation.

5

BACKGROUND

[0002] Optical coherence tomography (OCT) is an example of a technique using depth-resolved reflectometry, and enables the generation of three dimensional images of a sample. Low coherence interferometry is used to provide depth resolution of light backscattered from the

10 sample. OCT allows micrometer resolution and does not require the use of ionizing radiation, making it suitable for investigating biological samples.

[0003] Polarization-sensitive optical coherence tomography (PS-OCT) is a variation of OCT in which interference fringes are detected in two orthogonal polarization channels. This provides additional information on the sample. To allow a comparison between the incident and detected

15 polarization states, a bulk optic system may be used. However, in some applications an optical fiber system may be more convenient or necessary. Fiber optic systems may alter the polarization state of the light, such that the polarization state incident on the sample and the polarization state reflected from the sample may be unknown. This prevents determination of the fast-axis of the sample.

20 [0004] US 2008/0007734 describes a method using at least two unique incident polarization states to determine a relative orientation of the fast-axis of a sample.

BRIEF SUMMARY OF THE DISCLOSURE

[0005] In accordance with an aspect of the present invention there is provided a device for use 25 in producing a depth-resolved signal along an electromagnetic radiation path, the device comprising a delivery section arranged to emit polarised electromagnetic radiation; at least three reference surfaces arranged in a path of the electromagnetic radiation emitted by the delivery section.

[0006] The reference surfaces may be surfaces of at least a first retarder and a second

30 retarder. The reference surfaces may include: a first face of the first retarder, a second face of the first retarder, on an opposite side of the retarder to the first face, and a first face of the second retarder, wherein the first face of the second retarder does not face the first retarder. The retarders may include first and second quarter wave plates. A fast-axis of the first quarter wave plate may be oriented at 45° to a fast-axis of the second quarter wave plate.

2

[0007] The device may further comprise a separator for providing electromagnetic radiation to the delivery section and an interferometer reference section. The device may further comprise a polarisation sensitive detector for detecting interference between electromagnetic radiation returned from the reference section and electromagnetic radiation returned from the delivery

5 section. The device may further comprise a combining section for combining the electromagnetic radiation from the reference section and the electromagnetic radiation returned from the delivery section, wherein the combining section includes a polarizing beamsplitter, and a fast-axis of the retarder closest, of the first and second retarders, to the delivery section is oriented substantially parallel with a vertical transmission axis of the polarizing beamsplitter of

10 the combining section.

[0008] According to another aspect the invention provides a method of analysing data representing a depth-resolved signal along an electromagnetic radiation path, the method comprising receiving the data, wherein the data are based on an output from a polarisation sensitive electromagnetic radiation detection section, and the signal is associated with a sample

15 and a calibration section, the calibration section including at least three reference faces such that the reference faces and sample are arranged in the radiation path; determining, based on the received data, at least one of: an absolute orientation of a fast-axis of the sample, a completely specified Jones matrix for the sample, or a completely specified Jones matrix for the electromagnetic radiation path between the calibration section and the detection section.

20 [0009] The reference faces may include a first face of a first retarder, a second face of the first retarder, on an opposite side of the retarder to the first face, and a first face of a second retarder, wherein the first face of the second retarder does not face the first retarder.

[0010] A delivery section between the detector and the reference faces may receive radiation from the sample, via the reference faces, and deliver the radiation to the detector, and

25 determining may include determining Cayley-Klein parameters of Jout, where Jout is the Jones matrix of the delivery section between the calibration section and the detector.

[0011] Determining may comprise finding the true round-trip Jones matrix of the sample J's from Jc,m;s = J'outRiQi Ri 1R2Q2R21J s R2Q2R2 1RiQiRi 1 J'"10ut where Jc,m;s is the apparent round-trip Jones matrix of the sample, as measured through the first and second retarders, J'out and J's

30 are Jout and Js, respectively, multiplied by a rotation matrix mapping the measurement frame to a reference frame, Qi and Q2 are Jones matrices of the first and second retarders, and Ri and R2 are rotation matrices accounting for orientations of the first and second retarders, and wherein J'out is determined from: Jc,m= J'out Ri Q2i Rr1J'0Ut"1, and J'c,m = J'outRiQi Ri 1R2Q22 R2 R*iQ*iRi J out-

35 [0012] An aspect of the invention provides a computer program comprising instructions to cause, when executed by a computer, the computer to perform the above method.

3

[0013] An aspect of the invention provides a polarization-sensitive electromagnetic coherence tomography system comprising: the above device, and a processor arranged to execute the above computer program.

[0014] The embodiments of present invention have the aim of improving on, or providing 5 alternatives to, known devices and methods.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Embodiments of the invention are further described hereinafter with reference to the accompanying drawings, in which:

10 Figure 1 illustrates a system according to an embodiment of the invention.

Figure 2 illustrates a calibration section according to an embodiment of the invention. Figure 3a shows measured double-pass phase retardance and fast-axis orientation of a sample quarter wave plate as a function of set orientation relative to an orientation of a calibration section according to an embodiment of the invention.

15 Figure 3b shows Stokes vector equivalent to an optic axis measured using an embodiment of the present invention, presented on a Poincare sphere.

Figure 4a shows a structural image of a tendon and a calibration section according to an embodiment of the invention.

Figure 4b shows fibre orientation of equine tendon, measured using an embodiment of 20 the invention, as a function of set orientation relative to the orientation of the calibration section. Figure 5 is a flow diagram of a method according to an embodiment.

DETAILED DESCRIPTION

[0016] Polarization-sensitive optical coherence tomography (PS-OCT) can non-destructively 25 determine the optical birefringence of turbid materials such as biological tissue in a depth-

resolved manner (see, for example, J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, Opt. Lett. 22, 934 (1997) and N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage 17, 33 (2009)).

[0017] In fibre-based PS-OCT, source light is transmitted into the sample via an inward-30 directed Jones matrix Jin and backscattered light is transmitted back out to a detector (e.g. a polarizing beam-splitter in the detector) via an outward-directed Jones matrix Jout- The desired Jones matrix of the sample, Js, is thus measured indirectly via the matrix-product Jm = Jout Js Jin-

[0018] The arrangement may be calibrated (see e.g. B. H. Park, M. C. Pierce, B. Cense, and J. F. de Boer, Optics Letters 29, 2512 (2004)). For example, the calibration may include

35 measuring the apparent Jones matrix of a reference reflecting surface that by definition has

4

Js = 1 and hence yields the product Jm,R = J0UtJin- Inverting this matrix and multiplying the sample measurement Jm by it thus yields the calibrated Jones matrix Jc,m

[0019] *^c,m *^out*^s*^out *^U

( .. n ^

pyen,L 0 0 p2e

-irjl 2

JU> (1)

[0020] where Ju, p-\, P2 and q are a general unitary matrix, two transmittances of the

5 eigenvectors of the sample, and the phase retardance of the sample, respectively. Calibration using a reference reflector thus eliminates the effects of Jin however the measured sample Jones matrix is still not directly obtained because of the multiplication by the unknown Jout,

which will be representable in the absence of fiber diattenuation as an arbitrary special-unitary matrix of the form (e'^cosd -e'^sinS; e'^sinS e'^cosd), where {<p, (//, 9} are termed the Cayley-10 Klein parameters. The phase retardance can therefore be extracted accurately without knowledge of Jout through the phase difference of the resulting diagonal elements since Jc,m is unitarily similar to Js. However the sample orientation is not directly obtainable unless full knowledge of Jout is also available. In the absence of this information then since the eigenpolarizations of Jc,m (i.e. column vectors of Ju) are not, in general, linear states there is no 15 simple way to extract the orientation from them.

[0021] Equation 1 allows the relative measurement of optic axis. Thus, the relative orientation between two different positions on a sample may be measured (where "orientation" refers to the orientation of the optic axis). One approach to making the orientation measurement absolute would be to measure the relative orientation between the sample and a calibration wave plate of

20 known orientation. Since both measurements must be made through the same Jout this either requires the wave plate to be inserted and then removed or for it to cover a portion of the field of view (for example). Inserting and removing a wave plate of known orientation may lead to an increase in complexity, and may not be possible in some applications. On the other hand, the field of view of the device would be reduced if the wave plate permanently covers a portion of 25 the field of view. Moreover, the relative orientation obtained from Equation 1 possesses a sign ambiguity, so a complete determination of the orientation of the fast-axis is not possible.

[0022] Figure 1 schematically illustrates a PS-OCT system 100 according to an embodiment of the present invention. A light source 110 provides optical radiation. Figure 1 illustrates a swept source polarization sensitive OCT (SS-PS-OCT) device, and so light source 110 is a

30 swept source (SS). The present invention is not limited to SS-PS-OCT, and the light source is not required to be a swept source. The light source may include, for example one or more of superluminescent diodes, ultrashort pulsed lasers or supercontinuum lasers. A source section 115 includes the light source 110, and may also include optical elements such as a polarization controller, one or more polarizers, etc. to control the properties of the light. In Figure 1, the

5

source section 115 includes polarization controller 111, linear polarizer 112 and electro-optical modulator 113. Other optical elements for beam focusing, shaping and guiding, etc. may also be provided.

[0023] Light from the source section 115 is passed (e.g. via optical fibers) to 2x2 coupler. The 5 2x2 optical coupler is an example of a splitting section 140 for dividing the light source into at least two paths. One path is directed along a reference arm 120 and the other path is along a sample arm 130. Any suitable optical component may be used in the splitting section. In the embodiment of Figure 1 the splitting section directs light between the reference arm and sample arm in a 1:9 ratio. The splitting section 140 may include a polarizing beamsplitter.

10 [0024] An interferometry section includes the reference arm 120, sample arm 130 and splitting section 140, along with a combining section 145. Light from the reference arm 120 is combined with light from the sample arm 130 to allow extraction of a coherent signal from the sample arm 130. In some embodiments the path length of the reference arm 120 may be controllably adjusted to provide control over the coherent signal that is extracted, particularly in

15 embodiments using time domain OCT. The path length of the reference arm need not be adjustable in some cases, for example where techniques such as frequency domain OCT, Fourier domain OCT or swept source OCT are used.

[0025] The reference arm extends between splitting section 140 and combining section 145, via elements 121 to 124. The combining section 145 receives and combines the outputs from

20 the reference arm 120 and the sample arm 130. In some arrangements, a single beam splitter may form both the splitting section 140 and the combining section 145. In the embodiment of Figure 1, reference arm 120 includes one or more polarization controllers 121, a circulator 122, mirror 123, and linear polarizer 124. The reference arm may also include other optical elements, and in particular may include beam focusing, shaping and/or directing elements.

25 The end of the reference arm 120 is at beam splitter BS, which is an example of a combining section 145.

[0026] Sample arm 130 includes optical components, including delivery optics for delivering light from the splitting section 140 to the sample 150. The optical components of the sample arm 130 also includes a calibration section 170 comprising a plurality of reference surfaces. In

30 the embodiment of Figure 1 the sample arm includes polarization controller 131, circulator 132 and galvanometric mirror arrangement 133. The galvanometric mirror is an example of a beam controller for controlling a portion of the sample 150 that receives incident light. Other optical components, such as focusing elements, beam shapers and/or redirectors may also be provided.

35 [0027] Light scattered by the sample 150 is then directed to the combining section 145. In the

6

embodiment of Figure 1, the light from the sample 150 is returned along part of the sample arm 130 to circulator 132, and is directed from the circulator 132 to the beam splitter BS. As noted above, in some embodiments the splitting section 140 and the combining section 145 may be a single element, such as a beam splitter.

5 [0028] In the arrangement of Figure 1, Jin is the Jones matrix of the inward optical path (i.e. towards the sample) between the output of the source section 115 and the input to the calibration section 170. Jout is the Jones matrix of the outward optical path (i.e. away from the sample) from the output of the calibration section 170 to the input of the combining section 145.

[0029] Combined light from the reference arm 120 and the sample arm 130 is output from the 10 combining section 145 to a polarization sensitive detection section 160. According to the arrangement of Figure 1, the combining section 145 is a non-polarizing beamsplitter BS and the detection section 160 includes a pair of orthogonal polarizing beam splitters PBS. The two interferometric outputs of the non-polarizing beamsplitter are in antiphase thus allowing the two co-polarized signals from the polarizing beamsplitters to be used for balanced detection, as is 15 well known in the art.

[0030] The output from the detection section may be passed to a processing section 180. Processing section 180 may be a computer. The processing section may operate according to software instructions stored in volatile or not-volatile storage, such as RAM, ROM, optical disc, etc. Software instructions may also be received from a remote location, e.g. from a server via a

20 network connection.

[0031] According to the arrangement of the present embodiment, an absolute determination of the fast-axis of the sample may be obtained, even when the sample arm includes birefringent optical components. In addition, or alternatively, a Jones matrix for the sample 150 may be determined directly from the detected light reflected from the sample 150 and the reference

25 surfaces.

[0032] In a preferred embodiment, the reference surfaces are arranged serially between the delivery optics of the sample arm 130 and the sample 150, such that a light path from the delivery optics passes through each of the reference faces and is incident on the sample. Thus, light incident on the sample 150 has passed through each of the reference surfaces in turn

30 before reaching the sample 150. According to this embodiment, the reference surfaces do not reduce the field of view.

[0033] The reference surfaces may be retarders, such as wave plates, and are preferably arranged such that the fast axes of the retarders are non-parallel. The retarders may be substantially planar, and two opposite faces of a retarder may each be a reference surface.

35 [0034] As described below, when three reference surfaces are used, the Jones matrix of the

7

sample may be completely determined.

[0035] Figure 2 illustrates a calibration section 170 according to an embodiment of the invention. According to this embodiment, three reference surfaces are formed by a pair of quarter wave plates having respective fast axes at 45° to each other. A first quarter wave plate

5 171 has first 171a and second 171b faces, and a second quarter wave plate 172 similarly has first 172a and second 172b faces. The three reference faces are selected from these faces. In this arrangement, faces 171b and 172a directly face each other and the polarization of reflections from these faces is the same. Accordingly, only one of these faces is used as a reference face. In this embodiment the references faces may be 171a, 171b and 172b. 10 Alternatively faces 171a, 172a and 172b could be selected as reference faces.

[0036] Thus, the reference faces in this arrangement include both faces of one of the retarders, and one face of the other retarder. Each reference face is separated by a medium or components that are optically isotropic (non-birefringent). For example, none of the reference faces face toward each other across an air gap.

15 [0037] Light reaches the sample 150 after passing through the quarter wave plates 171, 172. Light scattered by the sample 150 then returns to the delivery optics via the quarter wave plates in the reverse direction. Herein, faces of the retarders 171, 172 facing the sample 150 and/or away from the delivery optics (along the optical path) are referred to as rear faces 171b, 172b, and faces of the retarders 171, 172 facing away from the sample 150 and/or towards the 20 delivery optics (along the optical path) are referred to as front faces 171a, 172a.

[0038] The calibration section 170 (e.g. the two sequential quarter wave plates of the arrangement above) allows additional information about the sample to be determined. Specifically, the signals measured from the front and back surfaces of each wave plate provide measurements that together allow Jout to be completely specified.

25 [0039] If the first quarter wave plate is oriented in space such that its fast-axis is "vertical" (i.e. in the same direction as that of the "vertically" polarized component in the detection optics (e.g. in the combining section 145) then after calibration the measured Jones matrix is J0UtHJ"10Ut, where H = (-1 0; 0 1). Substituting in the generic form for Jout, expressed in terms of the Cayley-Klein parameters gives:

[0041] Jcm contains only partial information on Jout, namely, the angle 0and the phase-angle difference £=</>-<//. Hence a calibration measurement using a single calibration waveplate is insufficient to determine all 3 Cayley-Klein parameters of Jout-

30 [0040]

cos 20 sin 20

sin20 -cos20 y

8

[0042] Where the quarter wave plate is immediately followed (i.e. without intervening birefringent elements) by a second quarter wave plate whose fast-axis is oriented at 45° to the first, it is possible to measure three reflections i.e. front of first plate, front of second plate and rear of second plate. This measurement may be performed by PS-OCT, in a similar manner to the measurement of a sample. The third measurement (i.e. from the rear of the second plate), after calibration using the first reflection, is thus:

*^c,m .2 *^out

1 (i , Y-l (A . Ji 0A R(tt/4) R(—TT/4)

>0 1 ,

0 1

Ji

[0043]

V" V V " V V" V

r

-i

V

sin 20 cos r\ -e1^ (cos 20 cos r\ +i sin 77)

-e~'^ (cos 20 cos 77 - i sin 77) - sin 20 cos 77

(3)

[0044] where R(0-i)=(cos0i sin0-i; -sin0i cos0i) is the 2-D rotation matrix. Eq. (3) contains information on q = </>+(// as well as £ & 20. Together with the matrix elements of Jc,m there is thus

10 enough information to completely specify Jout, with the physically irrelevant sign arising from angular wraparound effects. Since the measured reference-calibrated Jones matrix Jc,m;s of a sample with round-trip Jones matrix Js is:

[0045] J„,=J«QR(*/4))QR(-W4)JSR(W4)QR(-W4)Q.C, (4)

[0046] where Q is the Jones matrix for a quarter wave plate without rotation, knowledge of 15 Jout allows Js to be extracted from Jc,m;s- Jc,m;s is the apparent surface-calibrated sample Jones matrix, as viewed through the calibration section 170.

[0047] Clearly, as Jout may be determined, Jm,R = J0UtJin allows Jin to be found, giving complete knowledge of all birefringent distortions in the system.

[0048] The above analysis applies to a situation in which the "vertical" axis of the calibration 20 section 170 (i.e. the fast-axis of the first quarter wave plate) is vertically aligned, that is, the fast axis of quarter wave plate 171 is parallel to a reference direction in space, referred to herein as "lab vertical". Preferably lab vertical is established by correspondence with one of the two non-collinear states of linear polarization into which the analyzed electromagnetic wave is decomposed. In the arrangement of Figure 1, lab vertical may be parallel in space with the 25 vertical transmission axis of the polarizing beamsplitters in combining section 145.

[0049] The above analysis may be generalized to a situation in which the vertical axis of the calibration section 170 is not parallel to the lab-vertical. This may be the case, for example, if the calibration section 170 is housed in the end of an endoscopic probe. In this case the Jones matrices of the calibration section 170 (i.e. the reference surfaces) are no longer H and

30 QR(77/4)HR(-7t/4)Q, but R(£)HR(-0 and R(<T )QR(tt/4)HR(-7t/4)QRK ) where is the angular rotation of the calibration section's fast-axis relative to the lab vertical. Thus:

9

Jc,m;s = JoutR(C)QR(f)QR(^)R(-C)J,R(C)R(f)QR(^)QR(-C)Ji 100501 =J»QR(f)QR(-r)JlR(f)QR(-f)QJ:Bl (6)

[0051] where J'out=JoutR(<0 and J's=R(-<0JsR(<0- Since J'out is also a special-unitary matrix all of the previous analysis still applies except J'out is determined, rather than Jout, and J's is determined, rather than Js. Clearly J's is simply the sample Jones matrix but now expressed in a

5 reference frame that has rotated through an angle £"i.e. in a frame defined by the fast-axis orientation of the probe rather than the lab frame. Thus the arrangement achieves an absolute axis determination, in that the known probe orientation defines an absolute reference frame.

[0052] Typically, in interferometry, improved results are expected when the reference arm 120 and sample arm 130 are optically similar. In particular, where the chromatic dispersion in the

10 reference arm 120 is similar to that in the sample arm 130. In some embodiments the reference arm 120 may include compensating material to match (i.e. reduce a difference in) the dispersion in the reference 120 and sample arms 130. In embodiments, such as that in Figure 2, in which two retarders are used to provide the reference surfaces, the reference arm 120 may also include two retarders in the optical path. Where the retarders in the reference arm 120 are 15 (essentially) identical to those forming the reference faces, the dispersion in the sample arm 130 due to the calibration section 170 will be balanced by the retarders in the calibration section 170. Moreover, where the retarders in the reference arm 120 are arranged to cancel their birefringence, such that no net polarization is applied by the retarders over the round trip in the reference arm 120 (e.g. using two quarter wave plates arranged with 90° between their 20 respective fast axes) the polarization of the light received from the reference arm 120 is not affected by the presence of the retarders.

[0053] A method of determining Jout and/or Js according to an aspect of the present invention is illustrated in Figure 5. J'out and/or J's may be determined as well as, or instead of Jout and/or Js.

25 [0054] By way of illustration, a device according to the embodiment described above was used to measure the orientation of a sample quarter wave plate. The sample quarter wave plate was rotated from 0° to 180° in 10° increments, with respect to the fast-axis orientation of the reference quarter wave plate closest to the objective lens (the objective lens being part of the delivery optics closest to the calibration section 170 along the optical path). 128 depth scans 30 were averaged for each measurement. While the sample was rotated the calibration section 170 and the system fibers were not moved. Figures 3a and b show the measured double-pass phase retardance and the fast-axis orientation of the quarter wave plate using the Poincare sphere presentation method, respectively. The measured phase retardance of the quarter wave plate in Figure 3a was 170±5°, which are lower than the expected value of 180° due to the

10

phase wrapping effect (as described in M. C. Pierce, M. Shishkov, B. H. Park, N. A. Nassif, B. E. Bouma, G. J. Tearney, and J. F. de Boer, Optics Express 13, 5739 (2005)).

[0055] The measured fast-axis orientations, relative to that of the calibration section, are in good agreement with the expected values with a linear fitted slope of 0.98, showing that the 5 fast-axis orientation can be recovered accurately without ambiguity. This is further shown

Figure 3b in which a plane (line 310) determined by least-square fitting the resulting optic axes before calibration (circle 320) is rotated off the QU-plane of the Poincare sphere due to Jout-After calibration the plane is rotated back down onto the QU-plane indicating that Jout is cancelled out.

10 [0056] When using PS-OCT only the linear components of the sample properties can be measured due to the round-trip nature of detected light propagation in the sample. As a result, all possible sample optic axes lie on the QU-plane.

[0057] Figure 4 illustrates the use of a device according to an embodiment of the invention, with a birefringent biological tissue, equine tendon, as a sample. The fast-axis orientation of the

15 sample was measured as described above. The sample surface was oriented orthogonal to the incident beam. Figure 4a shows a structural image of the tendon along with the calibration section 170 containing two quarter wave plates, each with a thickness of around 115 |jm. White lines 471a, 471b, 472a and 472b correspond to front and back surfaces of the two quarter wave plates 171, 172. In order to increase measurement depth, quarter wave plates with small 20 thicknesses were used.

[0058] Figure 4b shows the measured fiber orientation of the tendon as a function of set orientation relative to the orientation of the calibration section 170. 50x50 image pixels were averaged for each orientation measurement. The averaging was used to increase the measurement reliability by reducing the uncertainty resulting from the system and the tissue

25 itself. The measured orientations are generally in agreement with the set values, showing that the calibration section 170 can be used to extract tissue fast-axis orientation without offset and sign ambiguity.

[0059] In the embodiments described above, the reference surfaces were faces of a pair of retarders. However, additional retarders may also be used. For example, three retarders may

30 each provide a single reference surface. The three surfaces may be provided in a single element. For example, three reference surfaces may be provided by a single element that has an internal face, such as when faces 171b and 172a of retarders 171 and 172 of Figure 2 are in contact.

[0060] The embodiments have been described as having three reference surfaces. Additional 35 reference surfaces may also be provided.

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[0061] The retarders in the above embodiments are quarter wave plates. Other types of retarders could also be used. Furthermore, the angle between the fast axes of the retarders is not limited to 45°. From symmetry considerations, using quarter wave plates at 45° to each other is expected to be a preferred arrangement.

5 [0062] In the general case, equations 2-4 become:

[0063] jcm = JouAQ^Jout (6)

[0064] Jcm = JoutRiQiRi R2Q2R2 ^iQi^i Jout (7)

[0065] Jc,m;s = JoutRiQi Ri1R2Q2R21Js R2Q2R21RiQiRi1 J 10ut, (8)

[0066] where Qi and Q2 are Jones matrices of the retarders, and Ri and R2 are rotation

10 matrices accounting for orientations of the retarders. As can be seen, symmetry considerations present in equations (2), (3) & (4) permit simplification of the equations for Jout , such that solving equations (2-4) is easier than solving equations (6-8). The generalization described in equation 5 is also applicable to this generalization, yielding:

[0067] Jc m = J out R, Q2! Rr1 JW1, (9)

15 [0068] J cm = J 0utRiQi Rr1R2Q22R21RiQiRr1 J 1out, (10)

[0069] Jc,m;s = J'outRiQi R1 1R2Q2R2 1J's R2Q2R2 1RlQlRl 1 J' 1out- (11)

[0070] Figure 5 illustrates a method 500 according to an embodiment of the present invention. The method begins at step 505, and at step 510 data representing a measurement is received. The measurement may be received from a device including a calibration section 170 and

20 polarization sensitive electromagnetic radiation detection section, as described above. In steps 515 to 525 Jc,m, J'c.m and Jc,m;s are determined based on the received data, as described above. Jout and/or Js is then calculated from the received data using Jc,m, J'c,m and Jc,m;s-

[0071] Steps 515 to 525 may be performed in any order. Furthermore, in some arrangements Jout and/or Js may be determined based on the received data without explicitly calculating Jc,m,

25 J'c.m and Jc,m;s- For example, where related quantities are calculated instead, or where the above equations for Jc,m, J'c,m and Jc,m;s are combined and solved simultaneously for Jout and/or Js. Alternatively, or in addition, an absolute orientation of the fast axis of the sample may be calculated in step 530 from the received data.

[0072] The data may be received directly from a detection section, such as section 180 of

30 Figure 1. Alternatively, the data may be received from a storage medium, such as a non-volatile storage medium. The data may also be received via a network.

[0073] The present invention may be applied to any OCT technique, such as time domain

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OCT, frequency domain OCT, swept source OCT, spectrum based methods, etc. Furthermore, the present invention may be applied in depth resolved methods other than OCT.

[0074] The present invention is described in relation to fibre-based PS-OCT, but may prove beneficial in when using optics that do not preserve polarization state other than, or in addition

5 to, optical fibres.

[0075] In some applications the interferometry section may be replaced with another section that allows depth-resolved information to be derived. For example, direct time-of-flight measurements may be used in some applications; particularly where long path lengths are used.

10 [0076] The reference surfaces are arranged such that reflections from each of the surfaces may be analyzed to extract information on the polarization of the reflections. Preferably, such that the analysis may be based on the depth-resolved technique to be used in analyzing the sample. According to the above embodiments, the reference surfaces are arranged such that a Jones matrix of the light path between the calibration section and the sample is known.

15 Preferably, the light path between the calibration section and the sample is free of birefringence and the corresponding Jones matrix is the identity matrix.

[0077] In the above embodiments the reference faces and sample are arranged sequentially in the light path. However, other arrangements are possible provided. For example a plurality of light paths may be present, each including one or more reference faces and/or the sample.

20 In this case, the differences between the light paths should be expressible as known Jones matrices (i.e. known a priori or capable of determination by some other independent means), with the exception of the effect of the sample on the light path (i.e. Js need not be previously known as this is to be determined). The above method may be applied to solve for Jout and/or Js, with suitable amendments to the equations to account for the non-sequential arrangement.

25 For example, a beamsplitter may be provided between the output of the delivery optics and the sample. One beam from the beamsplitter may be directed to the sample and the other directed to the reference faces. If the Jones matrices of these paths are known, the above approach may be applied to determine Jout and/or Js. If the additional paths (i.e. between the additional beamsplitter and the sample/reference section) are J0ut-samPie and Jout-caiib, respectively, and the

30 light path is air (for example) Jout-sampie = Jout-caiib and would be the unitary matrix. In such cases, the component(s) responsible for directing the light path(s) to the sample and reference faces (e.g. the beam splitter mentioned above) may be considered part of the calibration section. It is noted that a sequential arrangement is likely to be preferable in many cases, due to the structural simplicity provided by this arrangement.

35 [0078] Embodiments of the present invention have been described using optical radiation.

However, embodiments of the present invention could use any suitable form of electromagnetic

13

radiation, and are not limited to using optical radiation.

[0079] Throughout the description and claims of this specification, the words "comprise" and "contain" and variations of them mean "including but not limited to", and they are not intended to (and do not) exclude other moieties, additives, components, integers or steps. Throughout the

5 description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[0080] Features, integers, characteristics, compounds, chemical moieties or groups described 10 in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some 15 of such features and/or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

20 [0081] The reader's attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference.

25

14

Claims

1. A device for use in producing a depth-resolved signal along an electromagnetic radiation path, the device comprising:

5 a delivery section arranged to emit polarised electromagnetic radiation;

at least three reference surfaces arranged in a path of the electromagnetic radiation emitted by the delivery section.

2. The device of claim 1, wherein the reference surfaces are surfaces of at least a first 10 retarder and a second retarder.

3. The device of claim 2, wherein the reference surfaces include:

a first face of the first retarder,

a second face of the first retarder, on an opposite side of the retarder to the first face,

15 and a first face of the second retarder, wherein the first face of the second retarder does not face the first retarder.

4. The device of any preceding claim, wherein in use a sample is to be provided in the

20 electromagnetic radiation path, and the reference surfaces are arranged such that a Jones matrix of the electromagnetic radiation path between the calibration section and the sample is known.

5. The device of any preceding claim, wherein the retarders include first and second 25 quarter wave plates.

6. The device of claim 5, wherein a fast-axis of the first quarter wave plate is oriented at 45° to a fast-axis of the second quarter wave plate.

30

7. The device of any preceding claim, further comprising a separator for providing electromagnetic radiation to the delivery section and an interferometer reference section.

35

8. The device of claim 7, further comprising a polarisation sensitive detector for detecting interference between electromagnetic radiation returned from the reference section and electromagnetic radiation returned from the delivery section.

15

9. The device of claim 8, further comprising a combining section for combining the electromagnetic radiation from the reference section and the electromagnetic radiation returned from the delivery section, wherein the combining section includes a polarizing beamsplitter, and 5 a fast-axis of the retarder closest, of the first and second retarders, to the delivery section is oriented substantially parallel with a vertical transmission axis of the polarizing beamsplitter of the combining section.

10. A method of analysing data representing a depth-resolved signal along an electromagnetic radiation path, the method comprising:

receiving the data, wherein the data are based on an output from a polarisation sensitive electromagnetic radiation detection section, and the signal is associated with a sample and a calibration section, the calibration section including at least three reference faces such that the reference faces and sample are arranged in the radiation path;

determining, based on the received data, at least one of:

an absolute orientation of a fast-axis of the sample,

a completely specified Jones matrix for the sample, or a completely specified Jones matrix for the electromagnetic radiation path between the calibration section and the detection section.

11. The method of claim 10, wherein the reference faces include:

a first face of a first retarder,

and a first face of a second retarder, wherein the first face of the second retarder does not face the first retarder.

12. The method of claim 10 or claim 11, wherein a delivery section between the detector and the reference faces receives radiation from

30 the sample, via the reference faces, and delivers the radiation to the detector, and determining includes determining Cayley-Klein parameters of Jout, where Jout is the Jones matrix of the delivery section between the calibration section and the detector.

13. The method of claim 11, wherein determining comprises:

35 finding the true round-trip Jones matrix of the sample J's from

Jc,m;s = J'outRiQi Ri 1R2Q2R2 1J's R2Q2R2 1RlQlRl 1 J' 1 out

10

15

20

25

16

where Jc,m;s is the apparent round-trip Jones matrix of the sample, as measured through the first and second retarders, J'out and J's are Jout and Js, respectively, multiplied by a rotation matrix mapping the measurement frame to a reference frame, Qi and Q2 are Jones matrices of the first and second retarders, and Ri and R2 are rotation matrices accounting for orientations of 5 the first and second retarders, and wherein J'out is determined from:

Jc,m — J out Ri Q 1 Ri J out j and J c,m " J outRlQl Ri R2Q2 R2 R*|Q*|Rl J out-

10

14. A computer program comprising instructions to cause, when executed by a computer, the computer to perform the method of any one of claims 10 to 13.

15. A polarization-sensitive electromagnetic coherence tomography system comprising: the device of any one of claims 1 to 9, and

15 a processor arranged to perform the method of any one of claims 10 to 12.

16. A device substantially as described herein in relation to Figures 1 to 4.

17. A method substantially as described herein in relation to Figure 5.

20