A thermal light source technique for optical coherence tomography

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1 PRE-PUBLICATION Optics Communications 000 (2000) 000±000 A thermal light source technique for optical coherence tomography A.F. Fercher a, *, C.K. Hitzenberger a, M. Sticker a, E. Moreno-Barriuso b, R. Leitgeb a, W. Drexler a, H. Sattmann a a Institute of Medical Physics, University of Vienna, Waehringer Strasse 13, A-1090 Vienna, Austria b Instituto de Optica ``Daza de Valdes'' (CSIC), Serrano 121, E Madrid, Spain Received 24 January 2000; received in revised form 10 August 2000; accepted 9 September 2000 Abstract A new technique for optical coherence tomography imaging with spatially low-coherent light sources is presented. In this technique the low coherence interferometry (LCI) depth-scan is performed by the image of the light source, and, therefore, simultaneously by a multitude of mutually incoherent LCI channels, to increase the probe beam power. Thermal light sources have the advantage of extremely low time-coherence with coherence lengths in the 1 lm range. The performance of a tungsten halogen lamp with a thermal spectrum and a xenon arc lamp with broadened spectral lines superimposed on a thermal continuum are compared. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: Hz; Kb; d; Bj Keywords: Optical coherence tomography; Optical tomography; Low space coherence interferometry; Thermal light sources 1. Introduction The criteria for the use of a particular light source in optical coherence tomography (OCT) are: coherence properties, power, and wavelength of the emitted radiation. On this background two types of light sources can be distinguished. The light sources commonly used in OCT are oscillating in their transverse monomode. Corresponding light sources like superluminescent diodes (SLDs) and femtosecond lasers have low time-coherence * Corresponding author. Tel.: ; fax: address: adolf.friedrich.fercher@univie.ac.at (A.F. Fercher). and high space-coherence. But in general light sources can also oscillate in the transverse multimode. The multimode laser and spontaneously emitting light sources like the thermal cavity, the lament lamp, the halogen lamp, the electric arc lamp, and the gas discharge lamp are examples for the latter ones. These light sources have low spacecoherence and can have extremely low time-coherence. In this work we present a technique which uses besides low time-coherence also low spacecoherence and compare the performance of a tungsten halogen lamp and a xenon arc lamp in OCT. Standard OCT images are synthesized from low (time-) coherence interferometry (LCI) signals obtained by the so-called depth- or z-scan [1]. During the depth-scan the interferometer probe /00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S (00)00986-X

2 2 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 beam is directed onto the object and the backscattered light interferes with the interferometer reference beam. The complex degree of the timecoherence plays the role of a longitudinal or depth point spread function, its full width at half maximum (FWHM) de nes depth resolution in OCT [2]. For Gaussian light, OCT depth resolution is Dz ˆ cs c 2 ˆ 2ln2 k 2 p Dk ˆ lc 2 : 1 s c is the FWHM coherence time, l c is the FWHM coherence length, k is the mean wavelength, and Dk is the spectral wavelength width. High depth resolution in OCT demands for large bandwidth of the light source. First implementations of the OCT principle used SLDs at k ˆ 830 nm. These diodes yield coherence lengths in the 10-lm range and a beam power in the 10- mw range. A depth resolution Dz of 17 lm inair has been reported by Huang et al. [1]. Their small size and ease of operation made SLDs to the most popular light sources in OCT. To improve depth resolution in OCT as well as in optical low coherence re ectometry, a technique closely related to OCT, single quantum well (AlGa)As SLDs [3] with a tandem-type structure with two sections have been developed. Using these SLDs a depth resolution of 4.5 lm has been obtained in OCT [4]. In another approach to high depth resolution, spontaneously emitting light sources were used. For example, Youngquist et al. [5] use a laser diode operating at k ˆ 830 nm and biased well below threshold. A resolution of 10 lm has been obtained at a power of 20 lw. Using the same technique we have carried out rst measurements of the axial eye length using LCI and have obtained a resolution in the 10-lm range [6]. Clivaz et al. [7], for example, used the uorescence light from a Ti±sapphire crystal pumped by an argon laser. At a mean wavelength of k ˆ 780 nm a beam power of 4.8 lw has been obtained with a depth resolution of 1.9 lm. To improve depth resolution in high-resolution re ectometry and range-gating imaging Liu et al. [8] used a 4-W multiline Ar-ion laser pumped Rhodamine 590 dye jet and obtained a depth resolution of 2.9 lm at 9 mw beam power. OCT depth resolution has also been enhanced by using multiple sources. For example, Schmitt et al. used two light emitting diodes at peak wavelengths of 1240 and 1300 nm to synthesize a source with a short coherence length [9]. The outputs of the two diodes were combined in a single-mode coupler and yielded a depth resolution of 14.4 lm compared to 20.8 lm with only one of the sources. In a similar technique, Baumgartner et al. used a synthesized light source made up of two SLDs with mean wavelengths at k ˆ 830 nm and k ˆ 855 nm and obtained a depth resolution of 7 lm [10]. Bouma et al. [11] used a Kerr-lens mode-locked Ti:Al 2 O 3 oscillator at a mean wavelength of k ˆ 820 nm and obtained a depth resolution of 3.7 lm at an output power of 400 mw. Later, Bouma et al. [12] obtained a resolution of 6 lm using an all-solid-state Kerr-lens mode-locked Cr:forsterite laser operating at k ˆ 1:28 lm. More recently, Drexler et al. [13] presented an ultrahigh resolution OCT system using a Kerr-lens modulated femtosecond Ti:sapphire laser emitting pulses with a depth resolution of approximately 1 lm atk ˆ 800 nm and 1 mw power of the probe beam. 2. Thermal light coherence properties and optical coherence tomography technique Thermal light sources emit blackbody radiation with a spectral distribution given by PlanckÕs law for cavity radiation. The complex degree of timecoherence of blackbody radiation is obtained by a Fourier transform of PlanckÕs spectrum as c t ˆ90p 4X1 n ib 4 ; nˆ1 where b ˆ t k B T =h with k B denoting BoltzmannÕs constant, T the temperature, and h denoting PlanckÕs constant divided by 2p. Here the degree of time-coherence jc s jdecreases with a relaxation time of the order of s c ˆ h= k B T [14]. The corresponding coherence length can be estimated by cs c ˆ ch k B T : 2

3 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 3 Fig. 1. OCT device with a thermal light source. The LCI scan is performed by moving the object. AS, aperture stop; BS, beam splitter; CO, condenser; EP, entrance pupil of the interferometer; L, focusing lens; MF, multimode ber; OB, object; PD, photodetector; PO, photodetector optics; RM, reference mirror; XL, xenon arc lamp. In case of tungsten halogen lamps with typical temperatures of T ˆ 3300 K the coherence time is s c ˆ 2: s, and the corresponding coherence length is cs c ˆ 0:69 lm. This extremely short coherence length of thermal light is of great interest for OCT. Many thermal light sources, however, do not emit true blackbody radiation. Their radiation may be ltered by the surrounding media and by optical components transmitting the emitted light. Furthermore, the responsivity of the photodetector is decisive for the spectrum e ectively used in OCT. In addition, to provide interference between OCT reference beam and OCT probe beam spacecoherence is important. The complex degree of spectral space-coherence of blackbody radiation varies with sin k Dr = k Dr [14], where Dr is the distance between the two points on the source surface; k ˆ 2p=k is the wave number. This poor space-coherence is the main obstacle for the use of thermal light in coherent optics. In the interferometric scheme used in this work the source is imaged by the condenser on to the entrance pupil of the interferometer, see Fig. 1. In this case the illumination of the exit pupil of the condenser is e ectively spatially incoherent. The van Cittert±Zernike theorem [15] predicts a complex degree of space-coherence at the interferometer entrance pupil of c LS Dr ˆ2J 1 k DrN A ; 3 k DrN A where J 1 is the rst-order Bessel function, Dr is the distance between the two points in the source image. N A ˆ q=d is the paraxial numerical aperture of the interferometer, q is the radius of the interferometer aperture stop and D its distance from the entrance pupil. Obviously, Eq. (3) corresponds to the magnitude of the Airy pattern associated with the interferometer. As a consequence an entrance pupil diameter d larger than the central part of the Airy pattern associated with the system encloses a multitude of coherently illuminated source image spots. Points separated by more than the radius of the rst dark ring of the associated Airy pattern apart can be considered mutually incoherent. This distance can be de ned as transverse coherence-distance d c ±we use the term ``transverse coherence-distance'' in preference to ``transverse coherence-length'' to avoid possible uncertainties between the expressions ``coherence-length'' and ``transverse coherence-length:'' d c ˆ 3:832=kN A : 4 These coherent source image spots of diameter d c can be assumed mutually non-correlated. Note that d c equals RayleighÕs de nition of the resolving power of an image-forming instrument [15]. In the technique described in this communication the primary light source is imaged onto the interferometer entrance pupil. The interferometer entrance pupil represents the secondary light source of the interferometer. The LCI depth-scan is performed by the image of the secondary light source, formed by the focusing lens L at the object, see Fig. 1. This image consists of a multitude of coherently illuminated but mutually incoherent source image spots. Therefore, the OCT depthscan is simultaneously performed by many mutually incoherent ``LCI channels.'' The light of these channels overlaps during propagation but separates at planes optically conjugate to the interferometer entrance pupil. This technique has the potential of multiplexing many LCI depth-scans.

4 4 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 Each LCI channel can be detected by a separate photodetector positioned at a plane conjugate to the interferometer entrance pupil by using, for example, a photodetector array. This property also indicates a close relationship between the OCT technique presented here and the ``coherence radar'' technique. However, the coherence radar technique does not allow the application of heterodyne techniques [16]. Finally, in OCT a beam of reasonable power, for medical applications in the range of some lw to some mw, must be provided. In this respect a light emitting source can be characterized by its radiance, L, the energy ux per area A and the solid angle X of the radiation collected by the condenser. In air the energy ux of a Lambertian source with surface area A is U ˆ LAX [17]. For a plane circular Lambertian thermal light source of radius d=2 emitting radiation isotropically the van Cittert±Zernike theorem predicts a degree of coherence larger than 0.5 within an angle of w 6 2:215= kd=2 or within the solid coherence angle X C ˆ w 2 p=4; k is the mean wave number. Hence, the light energy ux emitted into the solid coherence angle is: U C ˆ LAX C ˆ 0:307Lk 2 : 5 The tungsten halogen lamp used in this work operates at a distribution temperature of about T ˆ 3242 K. From the Stefan±Boltzmann law the total radiated intensity emitted from a body at temperature T is I total ˆ grt 4, where g is the emissivity, that varies for di erent materials between zero and unity, and r ˆ 5: Wm 2 K 4. Hence, the maximal radiance is L max ˆ I total =2p and the maximal energy ux coherently emitted at k ˆ 0:85 lm is approximately 0.22 lw. The xenon arc lamp is a plasma lamp. It has broadened spectral lines superimposed to a thermal spectrum. The lamp used in this work operates at a temperature of about T ˆ 6000 K. Hence, even if we neglect the energy ux of the spectral lines, the xenon arc lamp is superior to the tungsten halogen lamp in terms of the maximal energy ux. Because of WienÕs displacement law and Eq. (5) an improvement in the coherently emitted energy ux of the thermal spectrum of 6000= :3 will be obtained. Including the energy ux of the spectral lines might increase the coherently emitted energy ux by a factor of approximately 2. Nevertheless, this low coherent energy ux demonstrates the dramatic lack of space-coherence of thermal radiation. Therefore, we combine several LCI channels to increase the probe beam power. 3. Methods and results In this work the LCI depth-scan is performed by the image of the secondary light source. Hence, all mutually incoherent LCI channels are combined to one LCI depth-scan beam thus increasing the probe beam power. As explained above the secondary light source consists of image spots of diameter d c which are mutually non-correlated. Hence, this technique is equivalent to simultaneously scanning the object by mutually non-coherent foci. Each coherent source image spot represents a separate LCI channel which contributes to the detector signal. As long as these contributions have the same phase they increase the detector signal. Phase variations can be caused by a tilted light remitting interface. Regularly re- ected light will then miss the photodetector optics aperture and reduce the corresponding depth-scan signal. In case of scattering objects, where scatterer from di erent depths contribute to the signal, speckle might occur and reduce the signal. Due to the extremely short coherence length of the light used here, however, this e ect may not play a dominant role. Besides demonstrating the increase of coherent ux we compare the performance of a tungsten halogen low voltage lamp (OSRAM 64625) and a xenon short arc lamp (OSRAM XBO 75) as light sources in OCT. The nominal size of the tungsten lament is 4:2 2:3 mm 2. The xenon arc has a size of 0:25 0:5 mm 2 ; its maximal intensity is emitted near the cathode. The object is a pellicle beam splitter with a geometrical thickness of approximately 2 lm. Fig. 1 depicts the optical scheme of the OCT interferometer. The depth-scan is performed by moving the object with the help of a stepper motor driven stage at 10 mm s 1. Con-

5 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 5 denser CO (focal length 30 mm) forms the secondary image of the light source at the entrance pupil EP (diameter d ˆ 0:1 mm) of the interferometer. Lens L (focal length 50 mm) forms the probe beam with the image of the entrance pupil at unity magni cation. This image is used to perform the LCI depth-scan. The aperture stop diameter is 2q ˆ 3 mm; its distance from the entrance pupil is D ˆ 100 mm; hence, the numerical aperture of the probe beam is N A ˆ 0:015. Due to the small numerical aperture only approximately eight mutually non-correlated source image spots were used. Probe beam powers were 1 lw with the halogen lamp and 3 lw with the xenon lamp. Photodetector optics PO forms an ``object image'' of the secondary image of the entrance pupil via the interferometer object arm at the photodetector. Similarly, a ``reference image'' of the entrance pupil EP of the interferometer is formed in two imaging stages via the interferometer reference arm at the photodetector. Interference occurs, if both, the ``object image'' and the ``reference image'' are spatially matched in size and orientation within the corresponding transverse coherencedistance d c and the path lengths are matched within the coherence-length l c. Then all coherent source image spots imaged via the object and the reference mirror nally overlap at the photodetector (multimode ber with 50 lm core diameter coupled to silicon PIN photoreceiver New Focus, Mod. 2001; gain set at ; Doppler frequency 22 khz). The electric photodetector signal is recorded with a personal computer. From the signals recorded the envelope has been computed to generate the OCT images. Pure data acquisition time of a 1 mm 10 lm image was approximately 2.5 s. As the x-scan had to be started manually, total acquisition time for one tomogram scan was approximately 15 min. It might be noticed, that the scheme shown in Fig. 1 resembles closely to LinnikÕs interference microscope [17]. However, the Linnik interference microscope uses fringes at the object surface image obtained at the interferometer exit to indicate the path di erences between the surface of the object and the surface of the reference mirror. In the OCT technique described here the object depth is scanned in transversely adjacent positions with the image of the light source and the signal of the photodetector at the interferometer exit is used to synthesize an OCT image. Fig. 2a and b depict the spectra of the two lamps used in the experiments. The responsivity of the photodetector extends from approximately 300 to 1100 nm with a maximum at approximately 875 nm. The spectrum of the tungsten halogen lamp has been obtained from a comparison with a 1000 W normal lamp. An Ulbricht-sphere technique was used with a double-prism monochromator and a photomultiplier as photodetector. The lamp Fig. 2. (a) Spectrum of the tungsten halogen low voltage lamp (OSRAM 64625), and (b) of the xenon short arc lamp (OSRAM XBO 75).

6 6 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 used in this work has a wavelength of maximal emission at 880 nm with a FWHM bandwidth of 510 nm. E ective spectra for the photodetector signal can be obtained by multiplying the lamp spectra with the spectral photodetector responsivity. The e ective mean wavelength of the halogen lamp appears shifted towards approximately 887 nm and the e ective bandwidth is reduced to about 320 nm. Hence, a depth resolution of approximately 1.1 lm has been obtained. The spectrum of the xenon lamp is the nominal spectrum as supplied by the producer of the lamp. It has large peaks in the wavelength range between 800 and 1000 nm where detector responsivity is maximal. Fig. 3 shows the real part of the mutual coherence function of the probe waves re ected at the pellicle and the reference mirror. The left part of each signal corresponds to the wave re ected at the anterior surface of the pellicle. It is the autocorrelation of the source light and de nes the OCT depth spread function of the corresponding light source. The right part of the signals shown in Fig. 3a and b represent the cross-correlations between the source light and source light transmitted twice through the pellicle. Both envelopes of the halogen lamp signal (Fig. 3a) are approximately Gaussian due to the approximate Gaussian spectrum of this lamp. The envelopes of the xenon lamp signal (Fig. 3b) deviate from this monotonic form. Their OCT depth spread function has a relatively narrow peak caused by the continuum of the spectrum superimposed on a broad background generated by the line spectrum of the xenon lamp. Hence, the FWHM concept to de ne the coherence length of the xenon light cannot directly be applied and, therefore, the depth resolution of 1.1 lm indicated in Fig. 3b is somewhat questionable. OCT images of the pellicle beam splitter are shown in Fig. 4. As described above, the depthscan has been performed with the image of the interferometer entrance pupil. The depth coordinate is geometrical depth times group refractive index. However, the group refractive index is not known. There are uctuations in the pellicle surface contour which we attribute to mechanical oscillations caused by infrasound. The performance of this technique can be characterized by its dynamic range. Dynamic range DR can be de ned by the ratio of the mean electrical signal power and the total electrical noise power DR dbš ˆ10log I 2 Signal =I 2 Noise ˆ 10 log SNR ; here I is electric current. The theoretical signal-to-noise ratio (SNR) for shot-noise limited detection is SNR ˆ 1=4 gpr= E Df ; g is the detector quantum e ciency, P is the probe beam power, R is the sample re ectivity, E is the (mean) photon energy, and Df is the noise equivalent bandwidth of the bandpass lter [18]. With a single mode of the halogen lamp we have P 0:11 Fig. 3. Real part of the mutual coherence functions of the probe waves re ected at the pellicle and at the reference mirror. (a) Halogen lamp, (b) xenon lamp. Dashed lines: envelopes. The left part of each envelope is the OCT depth spread function.

7 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 7 Fig. 4. OCT images (80 depth 108 transverse pixels) of a 2 0:5 lm thick nitrocellulose membrane with a nominal phase index of refraction of 1.5. Logarithmic gray scale. Front surface on top, back surface below. (a) Halogen lamp OCT; (b) xenon lamp OCT. Note: this gure demonstrates the high depth resolution of thermal light OCT. The true thickness of the membranes remains uncertain within the coherence length. lw because of transmission losses in the device (we used o -the-shelf optics without broad-band anti-re ection coatings). The theoretical dynamic range for shot-noise limited detection at an electronic bandwidth of 100 khz in this case is 60 db. With eight modes we have P 1 lw and a theoretical dynamic range of DR 70 db. Using a plane mirror as sample we measured 52 db with the tungsten halogen lamp. The gap between the experimental and the theoretical dynamic range is primarily caused by incomplete modulation of the data acquisition card (10 db) and furthermore by dispersion and polarization problems. For example, the beam splitter is not symmetric in the two beams and generates dispersion problems. In addition, polarization control is di cult in the converging probe and reference beams and has not been carried out. Therefore, to demonstrate the gain from the use of a multitude of spatial modes we slightly changed the illumination scheme of the interferometer to enable larger numerical apertures and replaced the xed aperture stop (AS in Fig. 1) by an iris stop with variable diameter 2q to adjust the numerical aperture. Also, to demonstrate the dynamics of this technique, we attenuated the light beam illuminating the interferometer by a 10 3 neutral density lter at the interferometer entrance pupil (EP in Fig. 1; 100 lm diameter) and used a second low-noise ampli er (Stanford Research Systems, Mod. SR 560) following the New Focus receiver, Mod Furthermore, the ampli ed electrical signal has been digitally ltered by a second order Butterworth lter with a bandwidth of 4 khz. As can be seen from Eq. (4) the coherent source image spot diameter d c is inversely proportional to the numerical aperture. Hence, the number of modes, as well as the probe beam power is proportional to the square of the numerical aperture. We obtained a dynamic range of DR ˆ 49 db with N A ˆ 0:016, DR ˆ 68 db with N A ˆ 0:052, and DR ˆ 73 db with N A ˆ 0:138. These data clearly demonstrate an increase of the dynamic range with increasing numerical aperture. This con rms the concept of the technique presented in this paper. At larger numerical apertures, however, asymmetries in the optical components become more important and hamper a corresponding increase of the dynamic range. 4. Conclusions A technique is presented which uses spatially incoherent light sources in the OCT depth-scan. The probe beam power is increased at the expense of transversal resolution. To increase the power of the probe beam the object is scanned by the image of the entrance pupil of the low-coherence interferometer thus combining approximately eight mutually incoherent light beams to one LCI depthscan beam. Probe beam powers in the 1 lw range were obtained at a transversal resolution of 100 lm. Higher probe beam powers can be obtained

8 8 A.F. Fercher et al. / Optics Communications 000 (2000) 000±000 with larger numerical apertures of the probing beam. For example, numerical apertures of N A ˆ 0:5 would yield probe beam powers in the 1 mw range at a transversal resolution of 100 lm together with a corresponding improvement of the dynamic range. Improving transverse resolution, however, would decrease the available probing beam power. For example, a transversal resolution of 10 lm would reduce the available probe beam power of a standard halogen lamp at N A ˆ 0:5 to about 20 lw. The technique presented here might be useful in cases with reduced demands on transversal resolution, like in the measurement of the thickness of tissue layers and in topographic measurements. Due to the large available bandwidth spectral OCT might also be a eld of application if reduced transversal resolution can be tolerated. Another possible application of the technique presented here is parallel OCT detection with smart one- and two-dimensional photodetector arrays [19]. Here each LCI channel can be associated to one photodiode. The attractive feature of the technique described in this communication is the fact that there is no loss of power when using many photodiodes because each photodiode can be associated with a separate light source point. Furthermore, the limited space coherence provides reduced cross-talk between the channels. Finally, this technique can also be used to obtain OCT images with (high-power) transversal multi-mode lasers. The performance of a tungsten halogen low voltage lamp (OSRAM 64625) and of a xenon short arc lamp (OSRAM XBO 75) as light sources in OCT have been compared in this work. A depth resolution of 1.1 lm was obtained in both cases. Whereas the xenon lamp provides a higher radiance than the halogen lamp the broad basis of its depth spread function will reduce contrast in OCT images. Furthermore, its irregular shape can produce artefacts in the OCT image. Acknowledgements We gratefully acknowledge nancial support from the Austrian Fonds zur Forderung der Wissenschaftlichen Forschung (project no ) and from the Jubilaumsfonds (project no. 7428) of the Austrian National Bank. References [1] D. Huang, E.A. Swanson, C.P. Lin, J.S. Schuman, W.G. Stinson, W. Chang, M.R. Hee, T. Flotte, K. Gregory, C.A. Pulia to, J.G. Fujimoto, Science 254 (1991) [2] A.F. Fercher, C.K. Hitzenberger, in: T. Asakura (Ed.), Springer Series in Optical Sciences, vol. 4, Springer, Berlin, 1999, pp. 359±389. [3] A.T. Semenov, V.K. Batovrin, I.A. Garmash, V.R. Shidlovsky, M.V. Shramenko, S.D. Yakubovich, Electron. Lett. 31 (1995) 314. [4] F. Lexer, C.K. Hitzenberger, W. Drexler, S. Molebny, H. Sattmann, M. Sticker, A.F. Fercher, J. Mod. Opt. 46 (1999) 541. [5] R.C. Youngquist, S. Carr, D.E.N. Davies, Opt. Lett. 12 (1987) 158. [6] A.F. Fercher, E. Roth, Proc. SPIE 658 (1986) 48. [7] X. Clivaz, F. Marqis-Weible, R.P. Salathe, Electron. Lett. 28 (1992) [8] H.-H. Liu, P.-H. Cheng, J. Wang, Opt. Lett. 18 (1993) 678. [9] J.M. Schmitt, S.L. Lee, K.M. Yung, Opt. Commun. 142 (1997) 203. [10] A. Baumgartner, C.K. Hitzenberger, H. Sattmann, W. Drexler, A.F. Fercher, J. Biomed. Opt. 3 (1998) 45. [11] B. Bouma, G.J. Tearney, S.S. Boppart, M.R. Hee, M.E. Brezinski, J.G. Fujimoto, Opt. Lett. 20 (1995) [12] B.E. Bouma, G.J. Tearney, I.P. Bilinski, B. Golubovic, J.G. Fujimoto, Opt. Lett. 21 (1996) [13] W. Drexler, U. Morgner, F.X. Kartner, C. Pitris, S.A. Boppart, X.D. Li, E.P. Ippen, J.G. Fujimoto, Opt. Lett. 24 (1999) [14] H.P. Baltes, in: H.P. Baltes (Ed.), Inverse Source Problems in Optics, Springer, Berlin, 1978, pp. 119±154. [15] M. Born, E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, [16] G. Hausler, M.W. Lindner, J. Biomed. Opt. 3 (1998) 21. [17] W.H. Steel, Interferometry, Cambridge University Press, Cambridge, 1983, pp. 30±31. [18] R. Muller, Rauschen, Springer, Berlin, 1990, p [19] S. Bourquin, V. Monterosso, P. Seitz, R.P. Salathe, Opt. Lett. 25 (2000) 102.