Improved digital holographic quantitative phase-contrast microscopy

Quantitative phase microscopy (QPM) is used in fields ranging from semiconductor industrial applications to biology. Among the existing QPM approaches, digital holography (DH) has emerged as a powerful technique. This is because it can provide both the full-field image of a sample in both intensity and phase, while allowing the accurate retrieval of refractive index maps, sample thickness, surface profiles and so on. A DH microscope (DHM) is essentially a conventional microscope with a modified optical configuration that uses a laser as light source. Its imaging system captures and stores a hologram that is numerically reconstructed to provide the image of the object. The remarkable DHM features provide a versatility that makes it ideal for many applications such as inspection of microstructures,¹ examination of living cells, characterization of waveguides, and mapping and monitoring electro-optic properties of photonic crystals. In addition, it provides a method for full numerical aberration compensation, extension of the focus-depth, reconstruction of tilted planes, etc.

A crucial problem, however, results from the parabolic shape of the wavefront emerging from the lens. This can be seen in Figure 1, shows sketches of the curved image wavefront of a flat surface with and without object.

The DH reconstruction process retrieves the entire field phase map. As a result, the object is ‘hidden’ by the parabolic curvature as qualitatively depicted in Figure 2 (a). Hence there is a need for a method to correct the phase map of the object by removing the field curvature, as shown in Figure 2(b).

Usually, this is achieved by subtracting a phase-mask obtained from a real or a synthetic digital hologram from the whole reconstructed phase map. The generation of a proper phase-mask, however, can be a cumbersome task. For instance, it involves recording a second hologram of an adequately flat sample area (not always available) or using time-consuming mathematical procedures, starting with the accurate measurement of the set-up parameters.^2–5

We have developed an alternative method that performs the phase measurement by combining DH and lateral shear interferometry (LSI),⁶ a well-known optical testing technique. The method only requires the recording of the sample hologram and can be applied to both transparent and opaque objects. The core concept is based on numerically shifting (i.e. shearing) the reconstructed complex wavefield on the DH reconstructed image plane, then subtracting it from the original wavefield. The procedure yields a numerical interferometric shearogram from which the phase-map of the sample can be fully retrieved.⁷ Essentially, shearing and the subsequent subtraction operation provide the derivative of the phase-map along the direction of the shear. The parabolic term is transformed into a linear term in the shearogram by the derivative. This linear term can then be simply removed before proceeding with integration procedures that finally yield the QPM map. Figure 3 summarizes the difference between the methods.

Our work shows that the DH-LSI method can be applied in both materials science and biology.

For example, Figure 4 shows the profile measurement of a microstructure consisting of two cantilevers 20 µm wide, 100 µm and 200 µm high, and strongly bent as a result of a fault in the fabrication process. (Sample: ST Microelectronics, Italy).

Figure 5 illustrates the application of the method on a living mouse cell. In this case, shearing along both x and y directions is required.