We present another step in our efforts to expand far-field imaging beyond the diffraction limit and beyond the limitations imposed by fluorescent labels. The model system we examine is based on the exploitation of entangled photon pairs at 810 nm generated by spontaneous parametric down conversion (SPDC) of a 405 nm source to resolve the separations of the line pairs of a series of two-dimensional objects. A ghost-imaging optical system directs signal and idler photons along two paths, one of which contains the objects. Images are constructed using a covariance analysis of the entangled pairs using typically 106 frames collected with an EMCCD detector that was calibrated to account for the number of entangled pairs of photons, which is necessary for an accurate determination of the resolution and its comparison with the classical method. Conservation of momentum requires that there is inversion symmetry between the transverse k vectors of the photons passing through the target and their entangled counterparts directed along the targetless path. Our covariance analysis not only addresses this symmetry but also that the width of the covariance peak is broader than a single pixel owing to the nature of SPDC and the details of the optical arrangement. Consideration of this broadening provides significant improvement of the image quality. The Heisenberg limit (HL) is achieved within experimental error: using the same optical alignment, the resolution obtained with entangled pairs of 810 nm photons is, within experimental error, twice that obtained with classical 810 nm photons. More importantly, the error bars of measurements with 810 nm entangled pairs are quantified by the Cramér-Rao lower bound (CRLB) and compared with those of the classical measurements. While other workers have done quantum imaging on nonpoint sources, to our knowledge we are the first group that not only has done the quantum imaging but also has compared the CRLB and the measured error of the quantum and classical measurements for a series of different-sized objects. (Similar comparisons have, however, been made for systems that can be approximated as point sources, e.g., determining the separation of two laser beams).
We present another step in our efforts to expand far-field imaging beyond the diffraction limit and beyond the limitations imposed by fluorescent labels. The model system we examine is based on the exploitation of entangled photon pairs at 810 nm generated by spontaneous parametric down conversion (SPDC) of a 405 nm source to resolve the separations of the line pairs of a series of two-dimensional objects. A ghost-imaging optical system directs signal and idler photons along two paths, one of which contains the objects. Images are constructed using a covariance analysis of the entangled pairs using typically 106 frames collected with an EMCCD detector that was calibrated to account for the number of entangled pairs of photons, which is necessary for an accurate determination of the resolution and its comparison with the classical method. Conservation of momentum requires that there is inversion symmetry between the transverse k vectors of the photons passing through the target and their entangled counterparts directed along the targetless path. Our covariance analysis not only addresses this symmetry but also that the width of the covariance peak is broader than a single pixel owing to the nature of SPDC and the details of the optical arrangement. Consideration of this broadening provides significant improvement of the image quality. The Heisenberg limit (HL) is achieved within experimental error: using the same optical alignment, the resolution obtained with entangled pairs of 810 nm photons is, within experimental error, twice that obtained with classical 810 nm photons. More importantly, the error bars of measurements with 810 nm entangled pairs are quantified by the Cramér-Rao lower bound (CRLB) and compared with those of the classical measurements. While other workers have done quantum imaging on nonpoint sources, to our knowledge we are the first group that not only has done the quantum imaging but also has compared the CRLB and the measured error of the quantum and classical measurements for a series of different-sized objects. (Similar comparisons have, however, been made for systems that can be approximated as point sources, e.g., determining the separation of two laser beams).
In this work, pairs of entangled photons are aimed at two spatially separated detectors: the path to one detector contains a physical object, while the path to the second detector does not. Yet, the second detector can be used to create an image of the object, even though none of the photons arriving at that detector have ever interacted with the object! This “ghost” imaging takes advantage of information that is shared between entangled photon pairs. This work aims to explore the underlying principles in a ghost imaging system that utilizes spontaneous parametric down-conversion (SPDC) as the source of entangled photons, with the larger goal of understanding the principles and operation of key parts of the system.
The method of optical centroid measurement (OCM) has shown to exhibit spatial super-resolution with enhancements at the Heisenberg limit in plane wave interference experiments. In this work, the OCM method is for the first time used in an imaging setting where actual object features are observed. The OCM result is rederived in a near-field imaging formalism for a general imaging system and in full 2-D treatment. Analogies to coherent and incoherent imaging are shown Moreover, coherent OCM imaging is experimentally implemented for photon number N = 2, where an experimental setup is presented which allows to generate the desired entangled two-photon state containing the super-resolved image. This state is then imaged by an imaging system with a finite resolution defined by its point spread function (PSF). The centroid measurement of the two-photon states delivers then an image with a width of the PSF reduced by a factor 2 corresponding to the Heisenberg limit. In the experiment, the object is illuminated by a continuous-wave pump laser centred at 405nm with an output power of 30mW. A 4-f lens system images the object to the state preparation output plane. In the far-field plane between the lenses, a 5mm long periodically poled KTiOPO4 non-linear crystal generates photon pairs at 810nm by type-0, frequency-degenerate and collinear spontaneous parametric down-conversion. This generated OCM state is then imaged by a single lens and detected in coincidence by a fully digital 2-D sensor array with single-photon sensitivity and per-pixel sub-nanosecond time resolution. The OCM state is spectrally filtered at 810nm. Its imaging capability is compared to classical light sources including spatially coherent, monochromatic illumination at 405nm and 810 nm, as well as spatially incoherent light at 810 nm. The former is implemented using collimated lasers, the latter is a thermal light source spectrally filtered at 810 nm. The PSF of the different light sources are compared at low numerical aperture by imaging a focal point of 25μm Gaussian waist radius.
In traditional ghost imaging, the entangled photon pairs produced from the spontaneous parametric down conversion (SPDC) process are used. There is an intrinsic disadvantage that the utilization efficiency of the photon pairs is very low. Inasmuch as all the correlated photon pairs produced by the degenerate SPDC process can be used to record the image of an object, the ghost imaging scheme we present here has a higher utilization efficiency of the photon pairs. We also investigate the robustness of our experimental scheme. The experimental results show that, no matter whether the photon-pair source is two light cones or two beam-like spots, the clear image of the object can be obtained. The slight rotation of the nonlinear crystal has no influence on the imaging quality. Our experimental results also demonstrate that when the part of the photon-pair source in the signal path or the idler path is blocked by unwanted things, the clear ghost image of the object can still be recorded.
The process of image recording is arguably one of the most prevalent technology in modern society and continues to inspire vast swathes of research due to its widespread applications spanning military, medical and consumer spheres. The danger present in a field so broad is that separate niches of research can become isolated with critical advancements struggling to traverse the gulfs between. Unifying the field is the omnipresent drive to acquire an ever increasing quality of images at the lowest possible cost, a goal which warrants continual fundamental research. Quantum entanglement exhibits many intriguing characteristics which make it a suitable tool for such fundamental investigations. The process of spontaneous parametric down- conversion has offered a yet unbeaten strength of photon correlations with the quantum nature of their production providing a reliable and controllable source of single-photons. Arising from these attributes is the technique known as ghost imaging. Though now known to be classically possible, the strength of entanglement generated correlations is yet to be surpassed. This thesis implemented this technique in tandem with the cutting edge detector technology in order to probe the fundamentals of image formation. This form of imaging allowed us to subject an object to a known number of photons whilst acquiring structural information from spatially separate, correlated photons which never interact with the object. The strength of the produced correlations allow us to acquire low background, high resolution images with far less light than traditional techniques and affords many novel benefits. The possibility of incorporating this technique with pre-existent regimes allowed me to draw from advancements made across the landscape of imaging research. Although referred to as “quantum ghost imaging” throughout this work, it should be noted that the intrinsic quantum nature of the correlations was not directly relied upon but provided an ideal source of strongly correlated photons. In order to determine the limits of a traditional imaging system this thesis first sought to answer the question: “can an image of an object be reconstructed from fewer photons than ii pixels in the image?” In chapter 3 I approached this from the perspective of compression, which minimises redundant information within a signal. This lead to the development of an imaging regime capable of imaging with far fewer photons than pixels in the image. By employing assumptions about the sparsity of natural images I was able to reconstruct an image of a biological sample containing an average of less than one photon per image pixel. Having reduced the number of photons necessary to form an image I then considered alternative methods for reducing the optical energy impinging on a sample. I sought to answer the question: “can non-degenerate ghost imaging reduce the optical energy impinged upon an object during imaging”. The photons produced in SPDC need not be of similar wavelengths, however may be chosen far from degeneracy, i.e. non-degenerate. In Chapter 4 I presented a ghost imaging system which illuminated the object with infrared light whilst recording the structural information via entangled visible photons. This allowed for objects opaque to visible light to be imaged in high quality without the need for a spatially resolving infrared detector, the state of the art of which lags behind their silicon based visible counterparts. I presented the systems capabilities by imaging objects which were etched into a gold substrate layered on to silicon, both of which are opaque to visible light. Not only did a reduction in energy deposition arise from the lower energy probe wavelength but applying the reconstruction techniques from the previous chapter brought that down to as low as ≈16 nJcm−2s−1. Seeking to expand the repertoire of applications, the low-light capabilities of my ghost imaging were applied to the technique of phase-contrast microscopy in chapter 5. Typically applied to translucent objects, phase-contrast imaging transfers phase information, i.e. the refractive index changed within the object, into an intensity distribution through the use of a phase-filter. In many of these applications the objects tend to be biological in nature, where high optical exposure can result in bleaching or damage. By applying the phase-filter non- locally, i.e. to the photons correlated to those probing the object, I acquired edge-enhanced images of a phase object whilst illuminating with significantly fewer photons than standard phase-contrast techniques. Having displayed the broad applicability of our low-light ghost imaging system, I then sought to determine the optical resolution in chapter 6. The resolution limits of ghost imaging are not clear at first glance owing to the resolutions dependence upon the strength of spatial correlations. As the length over which the spatial correlations are produced can be brought below the standard diffraction limit, it would seem the resolution of the system could be brought similarly low. To clarify this I artificially restricted the number of spatial modes in each of the correlated beams to uncover the physically realisable resolution. I show that although the resolution of a ghost imaging system to be fundamentally determined by the strength of the correlations, this can never be reached due to the inherent limitations of the intervening imaging system.
Relating to magnified image formation systems, we consider two processes in this work: quantum and classical incoherent imaging. There are similarities and differences between them. A similarity is that the optical transfer functions (OTFs) of both systems are obtained by calculating a correlation function. Concerning the differences, only two were found. The first difference is that, unlike classical incoherent imaging, quantum imaging with photon pairs generated by spontaneous parametric down-conversion is sensitive to the phase in the function which describes the object. The second difference is that the OTF of the quantum imaging system is a cross-correlation function of the OTFs of the signal and idler arms, while the OTF of the classical incoherent imaging system is an autocorrelation of the only pupil function existing in this case. We explore experimentally the second difference. We report the observation of a highly resolved image produced by a quantum light source in a setup where an incoherent light source is unable to spatially resolve the image of the object. The spatial resolution of the image is studied in a situation where the size of the object is magnified at the image.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.