Elsevier

Ultramicroscopy

Volume 138, March 2014, Pages 13-21
Ultramicroscopy

Information multiplexing in ptychography

https://doi.org/10.1016/j.ultramic.2013.12.003Get rights and content

Highlights

  • Demonstration of information multiplexing in ptychography, which we refer to as ptychographic information multiplexing (PIM).

  • PIM is capable to recover both different modes in illumination function and object function (also recovers relative intensity between the different illumination functions).

  • PIM could successfully be demonstrated in reflection and transmissionmode,  modes, for phase and modulus multiplexing respectively.

  • It could be demonstrated that the imaging performance when employing PIM compared to a single mode ptychographic experiment has hardly been affected.

  • PIM as demonstrated can be applied to many different fields such as in the visible (colour imaging, polarization imaging and optical metrology) and X-ray imaging.

Abstract

We show for the first time that ptychography (a form of lensless diffractive imaging) can recover the spectral response of an object through simultaneous reconstruction of multiple images that represent the object's response to a particular mode present in the illumination. We solve the phase problem for each mode independently, even though the intensity arriving at every detector pixel is an incoherent superposition of several uncorrelated diffracted waves. Until recently, the addition of incoherent modes has been seen as a nuisance in diffractive imaging: here we show that not only can the difficulties they pose be removed, but that they can also be used to discover much more information about the object. If the illumination function is also mode-specific, we show that we can also solve simultaneously for a multiplicity of such illumination modes. The work opens exciting possibilities for information multiplexing in ptychography over all visible, X-ray and electron wavelengths.

Introduction

The original motive for ptychography was to by-pass the resolution limits imposed by the poor focussing optics available at atomic-scale wavelengths (X-rays and high-energy electrons) [1]. A lens of small numerical aperture is replaced by a detector in the far-field. Provided the phase problem can be solved, the intensity over the detector can be used to construct a much larger synthetic aperture, allowing in theory wavelength limited resolution. Ptychography employs many (often hundreds) of diffraction patterns which are recorded from different areas of the same object, but where the areas of illumination overlap somewhat with adjacent areas. Redundancy in the data (information from each object pixel is expressed in many diffraction patterns) yields an extremely robust solution of the phase problem and can further be used to solve for the illumination incident on the object [2], [3], [4], perform superresolution imaging [5], obtain three-dimensional properties of the object [6] and to correct experimental errors which would otherwise corrupt the data [7], [8], [9]. In the last few years, ptychography has rapidly become an imaging method of choice in the synchrotron X-ray community, giving 2D images and tomographic reconstructions of materials and biological structures at unprecedented resolution and phase sensitivity [10], [11], [12], [13], [14]. It also has potentially wide applications in visible light imaging (even though very good focussing lenses are available) because the phase image it generates is quantitative, high contrast and extremely sensitive, leading to applications in live cell imaging [15], [16] and surface metrology [17], [18], [19].

In this paper we demonstrate experimentally for the first time an entirely new dimension in the ptychographic-imaging paradigm. We illuminate an object with three distinct wavelengths, all of which add in intensity in the diffraction plane. Until recently, this incoherent superposition of coherent modes in an experiment has been seen as problematic in ptychography: most phase-retrieval strategies fail completely if the assumption of perfect coherence is not met. Thibault and Menzel [20] have shown in model calculations that it is possible to use the redundancy in ptychography to infer modes within the specimen itself. Our experiments confirm this principle: furthermore, we not only solve for three independent images corresponding to the object's absorption and phase response at each wavelength, we also solve for three independent illumination functions (the probe-forming optics also has a different response at each wavelength) and also their respective spectral weights. We call the method ptychographical information multiplexing (PIM). The concept of information multiplexing has been demonstrated experimentally in digital holography [21], [22] (but here we have no reference beam), and has also been shown to be possible in model calculations using defocus (wave propagation) diversity [23]. Unlike holography, ptychography is extremely environmentally robust because with diffraction the specimen acts as its own reference.

Information multiplexing is enabled in ptychography thanks to its unique recording mechanism, where each object element is illuminated by several modes of illumination several times. When coupled with the diversity of the object across the range of illumination modes, which can be composed of any combination of temporal, polarized and spatial states, this allows an incoherent set of diffraction patterns to be separated out in the reconstruction process into several sets of coherent patterns. Although each individual diffraction pattern is an incoherent superposition, the different modes are separable because the information content is still recorded over the whole data set as a change of interference condition between two or more consecutive recorded diffraction patterns. This results in a change in how strongly data from one of the multiple signals is expressed in each recorded diffraction pattern. In this proof-of-principle we apply our method to a colour test object, a stained biological sample, and to a dual-wavelength configuration in reflection mode. Furthermore, the recovery of the spectral weights and the imaging performance is investigated.

Section snippets

Methods

Phase-retrieval is nowadays usually achieved by iteratively projecting between real-space and reciprocal-space constraints. In ptychography the real-space constraint is that the object and the illumination function remain constant for all exit-waves generated from the product of the object and the illumination at many relative displacements. In reciprocal-space, the Fourier constraint means that the estimated diffraction patterns (in both modulus and phase) must have a modulus which corresponds

Experimental work

The experimental samples have been carefully chosen to demonstrate the applicability of ptychographic information multiplexing in both transmission and reflection modes, for modulus and phase information multiplexing respectively. A diffuser was mounted between the light sources and specimen to obtain a better usage of the sensor's dynamic range and an increased spatial frequency response [26]. The diffraction patterns were recorded on a CCD sensor (Kodak KAI-04022; 2048×2048 pixels, pitch 7.4μm

Recovery of spectral weight

The influence of the initial estimate of the relative spectral weights on the recovered spectral weights has also been investigated. We used 28 different starting scenarios for the biological sample, as presented in Fig. 8. For each recovered probe the intensity value of all pixels has been summed up to give the power. The spectral weight represents the fraction of the probe's contribution to the sum of all recovered power contributions. Finally, the wavelength specific quantum efficiency of

Imaging performance of PIM

In digital holography multiplexing comes at the expense of reduced signal to noise ratio [32] and more than an 8 times reduction in the space-bandwidth product compared to in-line holograms [33], [34]. We therefore also investigated the influence of multiplexing in ptychography on resolution, field of view (FOV) and signal to noise ratio (SNR). A USAF test target was used in a transmission mode setup. Seven different data sets have been recorded (d=57 mm, Np=1024×1024 pixels) as shown in Table 2

Conclusion

Until recently, all experimental work on coherent diffractive imaging (whether single-shot CDI or ptychography) has regarded any degree of partial coherence in the experiment as a problem. Methods have been developed to ameliorate these effects, but they have been directed at removing illumination incoherence in order to achieve a single image of the object, which is assumed to diffract all the underlying illumination modes identically [24], [35], [36]. Thibault and Menzel [20] have extended

Author contribution

D.C. conceived the concept of ptychographic information multiplexing, designed and conducted the experiment and obtained an initial proof-of-principle. D.J.B. proposed the reconstruction algorithm, wrote the code and undertook the reconstructions. D.C. analyzed the data, with the assistance of D.J.B., and compared it to conventional imaging techniques. D.J.B. wrote the methods section. J.M.R. and D.C. wrote the main body of the manuscript and directed the project.

Additional information

Some of the methods described in this paper are the subject of awarded and pending patents owned by Phase Focus Ltd, which is a spin-out of the University of Sheffield. J.M.R. is a Director and Shareholder of Phase Focus Ltd.

Acknowledgement

This work was funded by the EPSRC Basic Technology Grant no. EP/E034055/1; ‘ULTIMATE MICROSCOPY: Wavelength-Limited Resolution Without High Quality Lenses'.

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    These authors contributed equally to this work.

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