Ghost optical coherence tomography

We demonstrate experimentally ghost optical coherence tomography using a broadband incoherent supercontinuum light source with shot-to-shot random spectral fluctuations. The technique is based on ghost imaging in the spectral domain where the object is the spectral interference pattern generated from an optical coherence tomography interferometer in which a physical sample is placed. The image of the sample is obtained from the Fourier transform of the correlation between the spectrally-resolved intensity fluctuations of the supercontinuum and the integrated signal measured at the output of the interferometer. The results are in excellent agreement with measurements obtained from a conventional optical coherence tomography system.

performed in the spectral (wavelength) domain, based on measuring the phase relation between different wavelength components of a broadband light source in order to determine the distance to the sample under test [7]. A major benefit of spectral-domain OCT is that it does not require scanning along the sample direction allowing for significantly faster acquisition speeds compared to its time-domain counterpart. Spectraldomain OCT has been demonstrated using various types of light sources including broadband stationary and pulsed sources or swept-wavelength sources [8].
In parallel to the rapid development in OCT technologies, there has also been much recent interest in the unconventional imaging technique known as ghost imaging.
Ghost imaging is based on the principle of image creation from the correlation between a known structured pattern that illuminates an object and the total integrated intensity transmitted (or reflected) by the object [9][10]. The defining feature of ghost imaging is that neither of the beams alone actually carries enough information to reconstruct the image.
Rather, it is only by correlating the two measurements of the structured illuminating source and the integrated intensity from the object that an image can be generated. In this regard, the fact that the light actually detected from the object is an integrated intensity has also led to ghost imaging to be referred to as single-pixel imaging. A significant advantage of ghost imaging when compared to conventional imaging is that it is insensitive to distortions of the wavefront occurring after the object as only the total light intensity is measured [11], making it ideal for measurements in turbid media or in the presence of other noise. Ghost imaging can be performed using light sources with random spatial intensity patterns [12] or patterns which are controlled using e.g. programmable digital micro-mirrors [13][14][15][16].
Ghost imaging has also been extended to the temporal domain [17][18] and very recently in the frequency domain for real-time broadband greenhouse-gas spectroscopic measurements [19].
In this work, we combine the technique of OCT with the concept of spectral-domain ghost imaging to introduce a new methodology of ghost optical coherence tomography.
This method generates a "ghost" spectral interferogram from the correlation between the spectrally-resolved intensity fluctuations of the light source and the integrated signal measured at the output of an OCT interferometer where a physical sample is placed. As in conventional OCT, the image of the sample is then retrieved from the Fourier transform of the interferogram. As a proof-of-principle demonstration, we (i) characterize the relative displacement of a perfectly reflecting mirror and (ii) perform measurement of the thickness of a microscope cover glass. The results are in excellent agreement with those obtained from a conventional OCT setup. A significant advantage of the ghost OCT scheme is that it does not require any particularly sensitive detector or spectrometer at the interferometer output. This could be extremely useful in situations where the object to be measured is highly absorbing or diffusing, for samples with low damage threshold or and for imaging in spectral regions where sensitive detectors are not available.
We begin by illustrating the concept of ghost spectral-domain OCT. To this end, Figure 1 compares the schematics of a conventional spectral-domain OCT system ( Fig.   1a) and that of the ghost spectral-domain OCT approach (Fig 1b). In a conventional OCT system, the beam from a broadband light source is equally divided between the two arms of an equal path Michelson interferometer. The image of the object inserted in one arm is generated by measuring with a high-resolution spectrometer the spectral interference pattern resulting from the superposition of the beams reflected from the reference mirror and object. The axial resolution of the system is inversely proportional the spectral bandwidth Dl of the source as dz = 0.44l0 2 /Dl (for a Gaussian spectral envelope), where l0 is the light source center wavelength. The imaging depth on the other hand is set by the spectrometer resolution. In spectral-domain ghost OCT, the beam from a light source with random spectral intensity fluctuations is divided between a reference arm where the fluctuations are measured in real time and a test arm consisting of a Michelson interferometer where the object to be measured is placed. The high-resolution spectrometer at the output of the interferometer is replaced by a slow integrating detector with no spectral resolution. The 'ghost' spectral interference pattern produced by the presence of object in the interferometer is then given by the normalised correlation function C(l) between the reference and test arm signals defined by:     We next performed a second series of experiments using a dual-interface sample.
For this purpose, we replaced one of the mirrors in the interferometer by a 210 µm thick (optical thickness) microscope cover slip consisting of two air-glass interfaces and the optical path difference between the two arms was set to be c.a. 1mm. The Fourier transform of the resulting interferogram is shown in Fig. 5 both for the conventional OCT system (Fig. 5a) and the ghost OCT setup (Fig. 5b). The results are again in excellent agreement and the positions of the two air-glass interfaces can be clearly identified. The distance between the two interfaces is measured to be 220 µm (optical thickness) close to the nominal value of 210 µm provided by the manufacturer. In conclusion, we have experimentally demonstrated proof-of-concept ghost OCT in the spectral domain using a broadband, spectrally incoherent, supercontinuum source.

Ghost OCT
As in a conventional OCT setup, the resolution is determined by spectral bandwidth of the source. The imaging depth on the other hand is given by the spectral resolution with which the spectral fluctuations of the light source can be measured in real time (and therefore the total dispersion if fiber dispersive Fourier transform is used). No particularly sensitive detector or spectrometer is needed at the interferometer output, which could be a significant advantage when the object is highly absorbing or diffusing, when the sample under has a low damage threshold and does not tolerate high intensity, or for imaging in spectral regions where sensitive detectors are not available. Finally, we note that the method can be implemented both with classical light sources and entangled photon sources and that a computational version may be realized by using e.g. controllable frequency combs which would eliminate for the need of single shot spectral measurements to perform the correlation.