Quantitative Microscopy without Lenses
Aberration-free Imaging Using Iterative Phase Retrieval
- Fig. 1: A typical optical diffraction pattern as used in Ptychography.
- Fig. 2: Opto-mechanical schematic for lensless optical transmission microscopy (left) and a prototype hardware realisation (right).
- Fig. 3: A TruWave image of a commercial hydrated toric contact lens (left) and a portion of the edge of the same lens in a 3D plot format. The colour scales show thickness, increasing from blue through yellow to red.
- Fig. 4: Lensless reflection image from a semiconductor wafer. The TruWave Magnitude and Depth data are represented as brightness and colour, respectively.
- Fig. 5: Composite TruWave Magnitude and Depth images of live (top) and dead (bottom) adherent A549 human alveolar epithelial cells. Courtesy P. O’Toole, et al, University of York.
Minimisation of the geometric restrictions and image infidelities imposed by imperfect physical focussing devices has been the subject of microscopy research for many decades, as has the development of ways to recover information-rich phase data lost by detectors that are sensitive only to illumination intensity. A new method of lensless imaging based on an iterative phase retrieval algorithm is not bound by conventional lens-engineering paradigms, and opens up new possibilities for nano-imaging.
While visible light microscopes now boast resolutions beyond the wavelength limit, aberration-free microscopy at most other wavelengths remains an elusive goal. Moreover, information content conveyed via phase changes that are accumulated as the light travels through (or is reflected by) the specimen is generally lost, because most microscope sensors detect only the intensity of the impinging illumination.
Conventional visible light techniques designed to recover phase information, such as Zernike phase contrast microscopy and digital holography, are associated with artefacts and are therefore inherently qualitative in nature, or are associated with considerable additional experimental complexity.
Simultaneous quantitative phase microscopy and aberration elimination have recently been enabled by a lensless imaging method that has been rendered fully practicable by high-performance low-cost computer processors. Ptychography [1-4] is a non-holographic, non-interferometric and wavelength-agnostic iterative phase retrieval technique in which a series of diffraction patterns is recorded while an illuminating beam moves with respect to a user-defined region of interest on the specimen. The algorithm (Ptychographical Iterative Engine, or "PIE") reconstructs from these diffraction patterns not only the wave-function (magnitude and phase) that emanates (or is reflected from) the chosen area of the specimen, but also the complex wave-function of the illumination. The method can be implemented with system hardware no more sophisticated than a computer, a diode laser, a CCD detector, and a mechanism for moving the beam with respect to the specimen (fig.
Since the algorithm computes the beam characteristics, it works even in situations where the illumination function is highly complex or difficult to model. The size of the illumination "spot", while it should be confined in area, is not the key determinant of resolution. (For typical visible light applications, the spot size may be about 100 µm-200 µm.)
The absence of an objective lens can be a significant geometrical advantage. For example, it enables sub-micron visible light imaging at very large working distances (30 mm and beyond.) It should also provide much greater space in the conventionally small (~1mm) gap between the objective and specimen in a transmission electron microscope. This would permit the insertion of tools, such as an ion beam milling accessory for in-situ sample preparation.
More importantly, PIE  and its progeny , known collectively as the Phase Focus Virtual Lens, can provide fully quantitative, high-fidelity, and high-contrast microscope images that can be focused in the computer at any depth within the specimen after the acquisition is complete. While Virtual Lens image acquisition does not require the use of lenses (as in figures 3 and 4, for example) the technology may optionally be incorporated as an "add-on" to conventional microscopy hardware in a variety of lens-assisted configurations. Thus for figure 5, the Virtual Lens technology was integrated within a conventional Olympus BX41 platform.
In the visible light regime, phase sensitivity of approximately 0.02 radians is available to measure specimen thickness, refractive index, surface topography and dielectric constant. In all cases, arbitrarily large fields of view may be obtained without the need for "stitching" of adjacent areas. The Virtual Lens is now also being applied in X-ray microscopy synchrotrons, where resolutions below 10 nm are anticipated [5-7]. In the electron domain , resolution should no longer be limited by the physics of aberration correction electromagnetic lens systems, and quantitative phase information is expected to enable applications from stain-free cell imaging to magnetic and electric field measurement.
Some Visible Light Applications
In a typical acquisition, the Virtual Lens generates simultaneously both quantitative phase and absorption/reflection data (TruWave Depth and TruWave Magnitude images, respectively), the focal plane of each being selectable by the user, post-acquisition, at will.
Ophthalmic Lens Thickness Measurement
There is a need to measure the thickness of contact lenses in order to ensure adequate oxygen flux to the cornea, and to ensure that the finished product meets the required manufacturing tolerances. Many modern lens designs (particularly torics, used to correct astigmatism) have complex spatially-varying thickness profiles that are not well-characterized by conventional measurement methods. For example, hydrated lens dimensions are often extrapolated from dry lens dimensions. The Virtual Lens TruWave Depth image, however, can provide directly a thickness map of a lens in its fully hydrated state. The TruWave Depth data (fig. 3) provide thickness measurements of the whole lens with lateral resolution of ~6 µm, as well as higher-resolution (~1 µm) thickness maps of user-selected areas, such as a lens edge. In each case, thickness sensitivity is around 0.1µm.
Integrated circuit chips with ever-smaller feature sizes require increasingly precise metrology in order to retain high quality and low cost. Accuracy in certain metrology measurements (e.g.: layer-to-layer alignment in multi-layer structures) is limited by imperfections that remain in even the most sophisticated objective lenses. Lens-free semiconductor metrology (fig. 4) promises to enable accurate quality assurance for next-generation lithography processes.
Live Cell Imaging
A goal in long-term longitudinal live cell microscopy experiments is the elimination of toxic nuclear fluorescent stains. The Virtual Lens TruWave Depth image provides very high contrast without staining, and the high fidelity of the quantitative data is expected to enable improved capabilities for segmentation and feature extraction (fig. 5, courtesy P. O'Toole, et al. University of York.)
Visible light Virtual Lens microscopy with sub-micron lateral resolution, sub-nano meter depth sensitivity, and exceptional contrast-to-noise ratio is being applied in markets as diverse as ophthalmic lens metrology and cellular analysis. The very high fidelity and reproducibility of the quantitative data are expected to enable improved automatic image processing and analysis. Elimination of lenses promises to revolutionize very high performance applications such as semiconductor metrology that are currently limited by residual lens aberrations. Using mechanical stage translation, acquisition times are typically tens of seconds. However, scanning the illuminating beam with a galvanometer mirror should reduce times to fractions of a second.
At X-ray wavelengths, the Virtual Lens is expected to overcome limitations of X-ray optics components such as high-aspect ratio gold zone plates. At electron wavelengths a new design paradigm is expected to enable, for the first time, diffraction-limited resolution in electron microscopy, realizing at last the vision of Richard Feynman , the father of nanotechnology.
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 "I would like to try and impress upon you while I am talking about all of these things on a small scale, the importance of improving the electron microscope by a hundred times. It is not impossible; it is not against the laws of diffraction of the electron." Richard P. Feynman. There's Plenty of Room at the Bottom: An Invitation to Enter a New Field of Physics. Engineering & Science, California Institute of Technology, 23(5):22-36 (1960)
Dr. Ian Pykett (corresponding author)
Prof. John M. Rodenburg
Dr. Martin Humphry
Phase Focus Ltd.
University of Sheffield, UK