WO2002004925A1

WO2002004925A1 - Method and apparatus for determining one or more properties of a sample in optical coherence tomography

Info

Publication number: WO2002004925A1
Application number: PCT/AU2001/000737
Authority: WO
Inventors: Andrei V. Zvyagin; David D. Sampson; Jonathon B. Fitzgerald
Original assignee: The University Of Western Australia
Priority date: 2000-07-05
Filing date: 2001-06-21
Publication date: 2002-01-17
Also published as: AU2001265706A1

Abstract

The present invention relates to a method and apparatus (10) for determining the instantaneous value of one or more properties of a sample examined by means of an interference technique, such as optical coherence tomography. The apparatus (10) includes an interferometer (12) which produces an interferogram signal (14), a phase comparator (16), a voltage-controlled oscillator VCO (18) and a low-pass filter (22). The phase comparator (16), VCO (18) and low-pass filter (22) together form an feedback loop in the form of phase-locked loop (30) wherein an output (24) of the low-pass filter (22) is linearly related to a scatterer's velocity ξs in the sample. The apparatus also includes a phase shifter (32), a mixer (38) and a low-pass filter (42) which generate a reflectivity signal (44).

Description

METHOD AND APPARATUS FOR DETERMINING ONE OR MORE PROPERTIES OF A SAMPLE IN OPTICAL COHERENCE TOMOGRAPHY

This application is based on and claims the benefit of the filing date of US provisional application serial no. 60/216,372 filed 5 July 2001.

FIELD OF THE INVENTION

The present invention relates to a method and apparatus for determining the instantaneous value of one or more properties of a sample examined by means of an interference technique, such as optical coherence tomography, and is of particular but by no means exclusive application in measuring the velocity of a sample in scanning Michelson interferometry.

Existing techniques for assessing fluid flow in vessels in the human body and, simultaneously, the morphology of the associated tissue convey considerable diagnostic information. However, conventional imaging modalities, most notably laser Doppler veloσimetry, do not provide the micron-scale spatial resolution that is desirable to maximise diagnostic utility. Recently, Doppler optical coherence tomography, an extension of optical coherence tomography (OCT) , has been shown to be capable of micron- resolution, two-dimensional tomographic mapping of flow velocity and morphology. Doppler OCT has been applied to blood flow mapping in subsurface vessels in living animal tissues and human skin tissues. Doppler OCT is a hybrid of optical coherence tomography and laser Doppler velocimetry.

The key subsystem is a scanning Michelson interferometer in which broadband light returning from the sample and reference paths interferes coherently only over a small axial distance range that may be shifted by altering the optical length of the reference path. Moving scatterers in the sample impart a Doppler (frequency) shift f_s to scattered light proportional to the scatterer's velocity v_s , and given by f_s = 2v_sιt_s cos θ / λ₀ , where n_a is the refractive index of the scatterer, λ₀ is the mean wavelength of the broadband optical source, and θ is the angle between the direction of motion of the scatterer and the incident beam. Similarly, scanning a mirror in the reference path at constant velocity v_r imparts a Doppler shift f_r to the reference beam given by /. = 2v_r I λ₀. The frequency of the resultant interferogram /_int is either the sum or difference of f_s and f_r , depending on the relative directions of motion of the scatterers and the reference mirror, and, therefore, provides a local measure of v_s .

The envelope of the interferogram provides a local measure of the mean reflectivity at λ₀. To construct two- dimensional tomographic images, a beam is scanned across the surface of a sample to produce an interference signal, which can be recorded as a series of interferograms using analogue or digital techniques, or further processed electronically before being so recorded.

To date, velocity and reflectivity data have been extracted from the recorded interferograms by performing a fast Fourier transform, a 'short-time' Fourier transform or a Hubert transform, which has resulted in a large computational overhead and has so far prevented real-time operation. In existing OCT and Doppler OCT systems based on analogue post-detection techniques, fixed frequency narrow bandpass filtering of the detected interferogram is employed. When sample motion is present, for example due to gross movement or due to rapid and variable flows present in the majority of blood vessels, the centre frequency of the interferogram shifts in proportion to the sample velocity. , A wider detection bandwidth is required to accommodate the variable Doppler shift, with associated lower signal-to-noise ratio. The need to limit the detection bandwidth in order to obtain an adequate sensitivity (typically around 100 dB) , however, limits existing Doppler OCT techniques to mapping low-velocity (of the order of a millimetre per second) blood flows in microscopic vessels. One existing technique attempts to overcome this trade-off by mapping the velocities of moving scatterers in discrete bands by demodulating in parallel the interferogram at discrete frequencies within narrow- frequency bands, but is then limited to measurement of velocity averaged over a discrete band. Further, this technique requires complex electronics and potentially further data processing.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method and apparatus for determining the instantaneous value of one or more properties of a sample (such as velocity and reflectivity) from an interferogram by employing a feedback loop, and - in at least one embodiment - for obtaining velocity and reflectivity simultaneously.

The present invention provides, therefore, a method for determining the instantaneous value of one or more properties of a sample, comprising: generating an interference signal for said sample by means of interferometry, said interference signal having an interference signal frequency; and creating a feedback loop having said interference signal as an input and operable to generate an output signal having an amplitude that is a function of said interference signal frequency; whereby said feedback loop responds to changes in said interference signal frequency by changing said amplitude in accordance with said function, thereby permitting said interference signal frequency to be determined from said amplitude.

Thus, as the determination of the amplitude of a signal is a straightforward matter, the frequency can be determined from that amplitude in real time. The feedback loop ensures that the amplitude maintains the same relationship with the frequency as the frequency changes .

It will be understood by those in the art that the sample may be one or more scatterers within a larger sample, tissue or flow.

Preferably said function is a linear function.

Preferably said method includes determining the velocity of said sample from either a linear relationship between said velocity and said frequency or a linear relationship between said velocity and said amplitude.

Thus, the velocity of the sample can thereby also be determined in essentially real time.

Preferably said method includes : generating by means of said feedback loop a multiplication signal having a substantially constant amplitude and a frequency equal to said interference signal; phase shifting said multiplication signal by 270°; mixing said multiplication signal with said interference signal to produce a mixed signal; and determining the reflectivity of said sample from a low frequency component of said mixed signal, whereby said reflectivity is proportional to the square of the amplitude of said low frequency component.

Thus, the local reflectivity of the sample can also be determined from an amplitude, and therefore in real time.

Preferably said feedback loop comprises: comparing said interference signal with a comparison input signal and generating therefrom a comparison output signal; and modifying said comparison input signal according to the amplitude of said comparison output signal.

Preferably the method includes modifying the frequency of said comparison input signal to equal said interference signal frequency.

In this embodiment, said comparison output signal comprises or includes said output signal.

Preferably said comparison output signal comprises a control signal the amplitude of which is representative of or proportional to the frequency of said interference signal.

Preferably said interference signal constitutes an interferogram. Preferably said generating of said interference signal is by means of Michelson interferometry, and more preferably by Doppler optical coherence tomography (although it may also by means of non- Doppler optical coherence tomography) .

Preferably said comparing of said interference signal with said comparison input signal comprises comparing the respective phases of said interference signal and said comparison input signal.

Preferably said method includes low-pass filtering said comparison output signal. More preferably said comparison input signal is generated by means of a comparison input signal generator controlled by said comparison output signal. Preferably said comparison input signal generator has a free-running frequency, and the method includes determining said velocity from the frequency difference between said free-running frequency and the frequency of said modified comparison input signal. More preferably said velocity is linearly related to said frequency difference.

Preferably said comparison input signal generator is a voltage-controlled oscillator or voltage-to-frequency converter.

Preferably said comparing of said interference signal and said comparison input signal is by means of a phase-locked loop functioning as a tracking bandpass filter.

Preferably said method includes determining the amplitude (or magnitude) of the envelope of said interference signal and, more preferably, the reflectivity of said sample from said amplitude of said envelope of said interference signal.

In one embodiment, the method includes phase-shifting said modified comparison input signal, mixing said phase-shifted modified comparison input signal with said interference signal to form a mixed signal, filtering said mixed signal, and determining the amplitude of the envelope of said interference signal from said filtered mixed signal. More preferably, the method includes determining the reflectivity of said sample from said amplitude of said envelope of said interference signal.

The present invention also provides a method for performing optical coherence tomography, including the method for determining the instantaneous value of one or more properties of a sample described above.

Preferably the method for performing optical coherence tomography includes determining the velocity or reflectivity of said sample.

The present invention also provides an apparatus for determining the instantaneous value of one or more properties of a sample, comprising: generating an interference signal for said sample by means of interferometry, said interference signal having an interference signal frequency; a feedback loop having an input comprising an interference signal for said sample generated by means of interferometry and operable to generate an output signal having an amplitude that is a function of said interference signal frequency; whereby said feedback loop is configured to respond to changes in said interference signal frequency by changing said amplitude in accordance with said function, thereby permitting said interference signal frequency to be determined from said amplitude.

Preferably said function is a linear function.

Preferably said apparatus includes means for determining the velocity of said sample from either a linear relationship between said velocity and said frequency or a linear relationship between said velocity and said amplitude.

Preferably said feedback loop is operable to generate a multiplication signal having a substantially constant amplitude and a frequency equal to said interference signal, and said apparatus includes phase shifting means for phase shifting said multiplication signal by 270°, a mixing means for mixing said multiplication signal with said interference signal to produce a mixed signal, and filter means for passing a low frequency component of said mixed signal, whereby the reflectivity of said sample can be determined from said low frequency component, said reflectivity being proportional to the square of the amplitude of said low frequency component. Preferably said feedback loop comprises : comparison means for comparing said interference signal with a comparison input signal and generating therefrom a comparison output signal; and a comparison input signal generator for modifying said comparison input signal according to the amplitude of said comparison output signal.

Preferably the apparatus is operable to modify the frequency of said comparison input signal to equal said interference signal frequency.

Preferably said modified comparison input signal and said interference signal have a substantially constant phase difference, and, more preferably, substantially equal frequencies .

Preferably said interference signal constitutes an interferogram. Preferably said apparatus includes a Michelson interferometer for generating said interference signal, and more preferably a Doppler optical coherence tomography apparatus for generating said interference signal (though the apparatus may include a optical coherence tomography apparatus for generating the interference signal) .

Preferably said comparison means is operable to compare the respective phases of said interference signal and said comparison input signal. Preferably said apparatus includes a low-pass filter for filtering said comparison output signal. Preferably said comparison input signal generator has a free-running frequency, whereby said velocity can be determined from the difference between said free-running frequency and the frequency of said modified comparison input signal. More preferably said velocity is linearly related to said frequency difference.

Preferably said comparison means comprises a phase-locked loop functioning as a tracking bandpass filter.

Preferably said apparatus includes means for determining the amplitude (or magnitude) of the envelope of said interference signal. More preferably the apparatus includes means for determining the reflectivity of said sample from said amplitude of said envelope of said interference signal.

The present invention also provides an optical coherence tomography apparatus, including the apparatus for determining the instantaneous value of one or more properties of a sample described above.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the present invention may be more clearly ascertained, a preferred embodiment will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of an apparatus for determining scatterer velocity and reflectivity in Doppler optical coherence tomography according to a preferred embodiment of the present invention;

Figure 2 is a plot of the amplitude of the envelope for the apparatus of figure 1 and that of a prior art technique; Figure 3a is a plot of the amplitude of a recorded interferogram versus time for the apparatus of figure 1 when the reference mirror of a Doppler optical coherence tomography apparatus is scanned;

Figure 3b is a plot of the envelope of the interferogram of figure 3a;

Figure 3σ is a plot of the control voltage of the voltage-controlled oscillator of figure 1 during the measurement of the interferogram of figure 3a;

Figure 4a is a map of the reflectivity of a sample of flowing milk measured by means of the apparatus of figure 1;

Figure 4b is a simultaneously recorded map of the velocity of the sample of figure 4a measured by means of the apparatus of figure 1; and Figure 4c is a plot of a velocity profile of the sample of figure 4c and a parabolic fit to that profile.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT Figure 1 is a schematic diagram of an apparatus 10, for determining scatterer velocity of a sample in a scanning Michelson interferometry apparatus, according to a preferred embodiment of the present invention. The apparatus 10 is shown with a scanning Michelson interferometry apparatus 12. The interferogram signal 14 (with frequency /_int ) from the scanning Michelson interferometry apparatus 12 is fed into a phase comparator 16, which also receives input from a voltage-controlled oscillator (VCO) 18 having a free-running frequency f₀.

The phase comparator 16 generates a comparison signal 20 if the interferogram signal 14 is not synchronous with the free-running frequency f₀ of the VCO 18. The comparison signal 20 is passed through a low-pass filter 22; the filtered output 24 of filter 22 is used as a control voltage 26 for the VCO 18, which responds accordingly by adjusting the frequency of its output 28 (i.e. the comparison input signal) to be equal to the frequency of the original interferogram signal 14 and by adjusting the phase of its output 28 to be the phase of interferogram signal 14 shifted by slightly more than 90°, the additional amount being a linear function of the frequency difference

The phase comparator 16, low-pass filter 22 and VCO 18 together form a feedback loop in the form of phase-locked loop 30, which functions as a tracking bandpass filter.

When phase synchronism (or 'lock') is established, the comparison signal 20 includes a low frequency component with an amplitude linearly related to ( /„ — /_int ) and a high frequency component with a frequency of 2 /_int ; low-pass filter 22 removes the second component, so that the output 24 of filter 22 is linearly related to ( /„ — /_int ) • As the free-running frequency f₀ of VCO 18 is known, output 24 can then be used to determine the frequency /_int of the interferogram signal 14 and hence the scatterer's velocity v, ^•

The output 28 of the VCO 18 is fed into a phase shifter 32, which phase-shifts the VCO output 28 by approximately 270° to produce a phase-shifted VCO output 34 with the same phase as interference signal 14. Phase-shifted VCO output 34 and a second interferogram output channel 36 is fed into a mixer 38, which performs a double-balanced mixing of the phase-shifted VCO output 34 and interferogram signal 14. The mixed output 40 of mixer 38 is filtered by low-pass filter 42, to generate a reflectivity signal 44.

The reflectivity at a given depth in the sample is proportional to the square of the amplitude m(t) of the interferogram signal 14 at the time in the scan corresponding to that depth. The interference signal 14 s_int (t) comprises a high-frequency carrier component of frequency f_m- _t (which is a function of the scanner and sample velocities) modulated by a low-frequency component due to the amplitude variation and given by _* t) = m t) cos(2;r /_int) .

The purpose of the phase shifter 32 and mixer 38 is to retrieve m (t), which is proportional to the square of the reflectivity, in order to obtain the reflectivity distribution along the scanning axis. The standard technique for retrieving the desired low-frequency signal, is to multiply the interferogram signal 14 by a constant amplitude signal of the same phase, with subsequent low- pass filtering. Referring to figure 1, however, this multiplication signal is synthesized by taking the VCO output 28 (which is a constant amplitude carrier signal of frequency /_int phase-shifted by 90° relative to s_m- _t (t) ) and phase shift it by 270° by means of phase shifter 32 to produce the multiplication signal in the form of phase- shifted VCO output 34, which is back in-phase with the input interferogram signal 14. This multiplication signal (or reference signal) is given by s_raf (t) = cos(2;r /_int), where, for simplicity, the constant amplitude of this signal is set to unity. It can be shown that multiplication of these two signals, by means of mixer 38, results in mixed output 40, that is

«_.«•«-.<«)

+ ^{m(t) ∞s} " ^Λ

The low-pass filtering of mixed output 40 by means of low- pass filter 42 removes the second term in this equation leaving a term proportional to the square root of the local reflectance of the sample along the scanning axis .

In a conventional OCT system employing envelope detection at a fixed bandpass frequency, the optimal bandwidth of a fixed bandpass filter is a trade-off between axial resolution and sensitivity and is approximately 2Δ/, where Δ/ is the full-width half maximum power bandwidth of the signal. To pass the interferogram signal 14 through such a filter without significant attenuation, the Doppler shift f_s should not exceed Δ/ . For a Gaussian coherence function, Δ/ is given by Δ/ = 4 ln(4)v_r / π l_c , where l_c is the coherence length of the source and the corresponding velocity v° is:

π _cιιcos

This velocity can be compared with the maximum velocity obtainable with the apparatus of the present invention. The measurable velocity range depends on the ability of the phase-locked loop 30 to establish and maintain lock as the frequency f_mt of the interferogram signal 14 varies in proportion to the scatterer velocity v_s . The velocity range is directly proportional to the so-called capture range of the phase-locked loop 30, or_PLL, given by

^_PL ⁼ A f_cap / f_o ' where the frequency range over which the phase-locked loop can establish lock is /₀ ± Δ . The maximum measurable velocity v_s ^PLL is then _y PLL ₌ Ot_γ ^ _{^ ( 2 )} n_s cos θ Equations (1) and (2) show that for vf^LL to exceed v° requires l_c / λ ₀ > 3 for a typical value of α_PLL = 0.3. To compare the sensitivity of the apparatus 10 more rigorously to that set by a fixed passband filter, the envelope of the interferogram after optimal band-pass filtering was determined numerically. The filtered interferogram is found from

-/, -/,)• H_BP (f - f_r)] , where F^"1 denotes the inverse Fourier transform, G is the Fourier transform of the auto-correlation of the low-coherence light source, and H_BP is the transfer function of the second-order bandpass filter. For the apparatus 10, the filtered interferogram is given by

-^χ[G( - /. - /.) • H_LP {f - f, - /,) • cos φ ] ,

where H _LP is the transfer function of the low-pass filter 42 in the reflectivity path. The term cos φ is a function of f_tut ~ f_o ^and accounts for the fading effect in the phase- locked loop 30.

Figure 2 is a plot of the amplitude of the envelopes for the two detection techniques (set to have identical signal- to-noise ratio of 109 dB at zero Doppler shift) versus Doppler shift f_s (kHz) due to sample motion. The curve 50 corresponds to the technique of the present invention, while curve 52 is for the technique employing a fixed passband filter. The curves 50,52 are based on the following typical parameters: θ = 76°, λ ₀ = 840 nm , I₀=16 μm, n_s = 1.4, f_r = 95 kHz, v_r = 40 mm/s and _PLL = 0.3.

The plot of figure 2 is also calibrated in scatterer velocity v_e (mm/s), while mean velocity ranges Vb for blood flow in humans are indicated at 54 above the plot for flow in veins 56, arterioles 58, capillaries 60 and arteries 62.

Figure 2 demonstrates the superior sensitivity of the apparatus 10 at typical coherence lengths for flow velocities that exceed a few millimetres per second.

In order to test the apparatus 10, Michelson interferometry apparatus 12 was implemented as a Doppler OCT system in bulk optics. The Michelson interferometer was illuminated with a superlu inesσent diode with an output power of 2.4 mW and a spectral width of 20 nm centred at 840 nm. A plane mirror mounted on a linear translation stage operating at 40 mm/s was used in the reference arm, giving i_nt ~ 95 kHz. A single axial scan of a stationary glass plate placed in the sample arm was performed, representing a single point-like scatterer. Figure 3a is a plot of the amplitude (in arbitrary units) of the recorded interferogram versus time (ms), figure 3b is a plot of the corresponding envelope, and figure 3c is a plot of the input of the VCO 18 (shown as frequency shift _s(kHz) versus time (ms)), as the reference mirror was scanned.

Figures 3a, 3b and 3σ demonstrate that the modified phase- locked loop circuit accurately produces the envelope and fringe frequency of the interferogram. The system exhibited a high dynamic range of 98 dB, as well as large velocity range of from -20 to +20 mm/s and a velocity resolution of 0.25 mm/s. For this example, /₀ was offset from /_int = f_r . Under typical operating conditions, /„ is set to /. , which results in a detectable signal in the velocity channel only when the sample velocity is less than v_s ^PLL . The rise and fall times of the VCO output are determined by the bandwidth of the low-pass filter in the phase-locked loop, which also affects the signal-to-noise ratio of the velocity signal.

The sample arm of the Michelson interferometer was then replaced with a galvanometer-mounted mirror and lens configured to raster the incident beam across a sample, and to collect the back-scattered light. Cross-sectional imaging of diluted milk flowing through a glass pipe of 0.58 mm bore tilted at 76° with respect to the incident beam was performed. To minimise aberrations, the glass tube was polished to form an entrance window.

Figures 4a and 4b are simultaneously recorded maps of the reflectivity m² (dB) and velocity v (mm/s) of the flowing milk, respectively, as a function of position or distance d (mm) . Figure 4c is a plot of a velocity profile (solid line) averaged over four radial lines that pass through the centroid of the sample and are evenly spaced in angle. The good fit to a parabola (dashed line) is evidence that the velocity map correctly reproduces the laminar flow profile. The method and apparatus of the present invention have a number of further advantages. Monolithic phase-locked loops with bandwidths in excess of 50 MHz are readily available. Thus, using the present invention should enable real-time imaging of high and variable flow velocities (from a few tens of μm/s to a few m/s) without employing excess detection bandwidth. The method is inherently low in complexity and in hardware component count, and measures bi-directional velocities over a continuous range. Furthermore, because of the frequency tracking property of the phase-locked loop, reflectivity measurements should be less prone to motion artifacts that degrade the signal-to- noise ratio through Doppler shifting out of the filter passband in the envelope detector. This feature may also be advantageous for detection in OCT systems, enabling higher sensitivity imaging of morphology under unstable or dynamic conditions. These advantages suggest strong potential for the technique to be widely applied.

Thus, it may be possible with the method of the present invention to extend the bi-directional continuous velocity range into the metre per second regime and so enable in vivo blood flow mapping in major vessels.

Modification within the spirit and scope of the aforementioned invention may be readily effected by a person skilled in the art. It is to be understood, therefore, that this invention is not limited to the particular embodiments and methods described by way of example hereinabove.

Claims

CLAIMS :

1. A method for determining the instantaneous value of one or more properties of a sample, comprising: generating an interference signal for said sample by means of interferometry, said interference signal having an interference signal frequency; and creating a feedback loop having said interference signal as an input and operable to generate an output signal having an amplitude that is a function of said interference signal frequency; whereby said feedback loop responds to changes in said interference signal frequency by changing said amplitude in accordance with said function, thereby permitting said interference signal frequency to be determined from said amplitude.

2. A method as claimed in claim 1, wherein said function is a linear function.

3. A method as claimed in either claim 1 or 2, including determining the velocity of said sample from either a linear relationship between said velocity and said frequency or a linear relationship between said velocity and said amplitude.

4. A method as claimed in any one of the preceding claims, including: generating by means of said feedback loop a multiplication signal having a substantially constant amplitude and a frequency equal to said interference signal; phase shifting said multiplication signal by 270°; mixing said multiplication signal with said interference signal to produce a mixed signal; and determining the reflectivity of said sample from a low frequency component of said mixed signal, whereby said reflectivity is proportional to the square of the amplitude of said low frequency component.

5. A method as claimed in any one of the preceding claims, wherein said feedback loop comprises : comparing said interference signal with a comparison input signal and generating therefrom a comparison output signal; and modifying said comparison input signal according to the amplitude of said comparison output signal.

6. A method as claimed in claim 5, including modifying the frequency of said comparison input signal to equal said interference signal frequency.

7. A method as claimed in either claim 5 or 6, wherein said comparison output signal comprises or includes said output signal.

8. A method as claimed in any one of claims 5 to 7, wherein said comparison output signal comprises a control signal the amplitude of which is representative of or proportional to the frequency of said interference signal

9. A method as claimed in any one of claims 5 to 8, wherein said comparing of said interference signal with said comparison input signal comprises comparing the respective phases of said interference signal and said comparison input signal.

10. A method as claimed in any one of claims 5 to 9, including low-pass filtering said comparison output signal.

11. A method as claimed in claim 10, including generating said comparison input signal by means of a comparison input signal generator controlled by said comparison output s ignal .

12. A method as claimed in claim 11, wherein said comparison input signal generator has a free-running frequency, and the method includes determining said velocity from the frequency difference between said free- running frequency and the frequency of said modified comparison input signal.

13. A method as claimed in claim 12, wherein said velocity is linearly related to said frequency difference.

14. A method as claimed in any one of claims 11 to 13, wherein said comparison input signal generator is a voltage-controlled oscillator or voltage-to-frequency converter.

15. A method as claimed in any one of claims 5 to 14, wherein said comparing of said interference signal and said comparison input signal is by means of a phase-locked loop functioning as a tracking bandpass filter.

16. A method as claimed in any one of the preceding claims, wherein said interference signal constitutes an interferogram.

17. A method as claimed in any one of the preceding claims, wherein said generating of said interference signal is by means of Michelson interferometry.

18. A method as claimed in any one of the preceding claims, wherein said generating of said interference signal is by means of Doppler optical coherence tomography.

19. A method as claimed in any one of the preceding claims, wherein said generating of said interference signal is by means of optical coherence tomography.

20. A method as claimed in any one of the preceding claims, including determining the amplitude of the envelope of said interference signal.

21. A method as claimed in any one of claims 5 to 15, including phase-shifting said modified comparison input signal, mixing said phase-shifted modified comparison input signal with said interference signal to form a mixed signal, filtering said mixed signal, and determining the amplitude of the envelope of said interference signal from said filtered mixed signal.

22. A method as claimed in either claim 20 or 21, including determining the reflectivity of said sample from said amplitude of said envelope of said interference signal.

23. A method for performing optical coherence tomography, including the method for determining the instantaneous value of one or more properties of a sample as claimed in any one of the preceding claims .

24. A method as claimed in claim 23, including determining the velocity or reflectivity of said sample.

25. An apparatus for determining the instantaneous value of one or more properties of a sample, comprising: generating an interference signal for said sample by means of interferometry, said interference signal having an interference signal frequency; a feedback loop having an input comprising an interference signal for said sample generated by means of interferometry and operable to generate an output signal having an amplitude that is a function of said interference signa1 frequency; whereby said feedback loop is configured to respond to changes in said interference signal frequency by changing said amplitude in accordance with said function, thereby permitting said interference signal frequency to be determined from said amplitude.

26. An apparatus as claimed in claim 25, wherein said function is a linear function.

27. An apparatus as claimed in either claim 25 or 26, including means for determining the velocity of said sample from either a linear relationship between said velocity and said frequency or a linear relationship between said velocity and said amplitude.

28. An apparatus as claimed in any one of claims 25 to 27, wherein said feedback loop is operable to generate a multiplication signal having a substantially constant amplitude and a frequency equal to said interference signal, and said apparatus includes phase shifting means for phase shifting said multiplication signal by 270°, a mixing means for mixing said multiplication signal with said interference signal to produce a mixed signal, and filter means for passing a low frequency component of said mixed signal, whereby the reflectivity of said sample can be determined from said low frequency component, said reflectivity being proportional to the square of the amplitude of said low frequency component.

29. An apparatus as claimed in any one of claims 25 to 28, wherein said feedback loop comprises: comparison means for comparing said interference signal with a comparison input signal and generating therefrom a comparison output signal; and a comparison input signal generator for modifying said comparison input signal according to the amplitude of said comparison output signal.

30. An apparatus as claimed in claim 29, operable to modify the frequency of said comparison input signal to equal said interference signal frequency.

31. An apparatus as claimed in either claim 29 or 30, wherein said comparison output signal comprises or includes said output signal.

32. An apparatus as claimed in any one of claims 29 to 31, wherein said comparison output signal comprises a control signal the amplitude of which is representative of or proportional to the frequency of said interference signal.

33. An apparatus as claimed in any one of claims 29 to 32, wherein said modified comparison input signal and said interference signal have a substantially constant phase difference,

3 „ An apparatus as claimed in claims 31, wherein said modified comparison input signal and said interference signal have a substantially equal frequencies.

35. An apparatus as claimed in any one of claims 29 to 32, wherein said comparison means is operable to compare the respective phases of said interference signal and said comparison input signal.

36. An apparatus as claimed in any one of claims 29 to 34, including a low-pass filter for filtering said comparison output signal.

37. An apparatus as claimed in any one of claims 29 to 35, wherein said comparison input signal generator has a free- running frequency, whereby said velocity can be determined from the difference between said free-running frequency and the frequency of said modified comparison input signal.

38. An apparatus as claimed in claim 37, wherein said velocity is linearly related to said frequency difference.

39. An apparatus as claimed in any one of claims 29 to 38, wherein said comparison input signal generator is a voltage-controlled oscillator or voltage-to-frequency converter.

40. An apparatus as claimed in any one of claims 29 to 39, wherein said comparison means comprises a phase-locked loop functioning as a tracking bandpass filter.

41. An apparatus as claimed in any one of claims 25 to 40, wherein said interference signal constitutes an interferogram.

42. An apparatus as claimed in any one of claims 25 to 41, including a Michelson interferometer for generating said interference signal.

43. An apparatus as claimed in any one of claims 25 to 42, including a Doppler optical coherence tomography apparatus for generating said interference signal.

44. An apparatus as claimed in any one of claims 25 to 42, including a optical coherence tomography apparatus for generating said interference signal.

45. An apparatus as claimed in any one of claims 25 to 44, including means for determining the amplitude of the envelope of said interference signal.

46. An apparatus as claimed in claim 45, including means for determining the reflectivity of said sample from said amplitude of said envelope of said interference signal.

47. An optical coherence tomography apparatus, including the apparatus for determining the instantaneous value of one or more properties of a sample as claimed in any one of claims 25 to 46.