Classical phase contrast microscopy techniques allow only non-quantitative partial visualization of transparent samples. In recent years, a variety of techniques have appeared for complete phase determination with different levels of complexity. A new simple non-interferometric method able to provide real time quantitative optical path difference information is presented. It is based on the use of a refractive pyramid to measure the transillumination wavefront gradient using incoherent light.
In microscopy, unstained biological media are often transparent; in such cases, the full determination of cellular structures using transillumination light is only possible through measuring the imprinted changes in the wavefront generated by spatial variations in the refractive index. Interferometric techniques [1-3] have been applied for the quantitative determination of these samples although their disadvantages include their reliance on the use of temporal coherent light, sophisticated instrumentation, mechanical stability and complex data processing. An alternative is direct sensing, which avoids the need of combination with a reference beam. Self-interference techniques based on the use of gratings have recently been proposed [4, 5] to obtain the phase gradient for subsequent integration, the main advantages being the simpler setups involved, the removal of the dependence on temporal coherent and real time operation. However, their reliance on interferograms still present drawbacks.
The Pyramid Wavefront Sensor
To directly determine quantitatively the phase using a non-interferometric simple optical setup, we have propose  the use of the pyramid wavefront sensor (PWS) . Related with the Foucault-knife method, the PWS was introduced to detect atmospheric wave aberration in astronomy and it is based on generating the Fourier transformation of the optical perturbation on a given input-plane and its division on the Fourier plane. As figure 1 shows, the splitting is carried out by a four-sided refractive pyramid driving the divided beams in diverging directions from the optical axis.
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After the light has passed through the pyramid, an additional optical system re-images the input plane onto a new conjugate plane, where a CCD registers four laterally displaced images of the input plane. If a plane wave with propagation direction along the optical axis arrives to the lens L1, an Airy diffraction amplitude distribution will be generated on the pyramid (for simplicity a circular aperture limits the input plane) and four approximate uniform discs each of which with a quarter of the input intensity will be detected on the CCD thanks to the lens L2. If the propagation direction of the plane wave slightly changes, the amplitude will be unequally distributed and an intensity imbalance between the four sub-images will be registered as in a quad-cell position sensor.
More explicitly, two images, Sx and Sy proportional to the wavefront gradient in orthogonal directions can be obtained by combining the images, Ii. In the case of a general optical perturbation, each four corresponding pixels in Ii will function as a quad-cell and the sensor generate an array of signals proportional to the local gradient at each input plane coordinates. This gradient determination can be applied to the transillumination wavefront of a microscopic sample optically transported to the input-plane.
Instantaneous Dynamic Range Extension
A difficulty with the PWS is the saturation for high gradient values. This occurs, for example, when the tilt in the above plane wave is so high that the diffracted field occupies only one pyramid facet. A method to avoid it is to mechanically introduce a displacement of the pyramid in such a way that the apex follows a circular trajectory around the optical axis (whose radius will be responsible for the sensor gain and range) during the acquisition time. Other option that generates the same signal and valid for transparent objects is to induce an oscillation in the illumination beam. This solution can be refined to avoid the need for moving parts by the use of a source able to generate all the required tilted plane waves simultaneously and incoherently and can be easily implemented using an extended incoherent disc-shaped emitter.
Such a source can be modeled as a composition of elemental annular sources of different radius, each composed of points emitting independently. If placed in the front focal plane of a lens, each point will generate, on the exit pupil of the lens, a plane wave with the propagation direction determined by its lateral position coordinates. In this way, the PWS response to an elemental annular illumination source will be equivalent to the response of an oscillating pyramid following a circular path around the optical axis. Assuming a perfectly uniform emission, an analytic expression for the expected sensor response can be obtained by integration of the elemental annular responses with respect to the radius (fig. 2).
Universidad de Murcia
Departomento de Fisica (CIOyN)