Chapter 4 – Making Light Work Harder in Biology  139

is a label-​free method, which uses advanced computational algorithms to numerically focus

a sample, in effect using a virtual objective lens, and has been applied to investigating various

aspects of cell cycle changes (see Marrison et al., 2013).

Ptychography was originally developed for the analysis of x-​ray microscopy scattering data

(see Chapter 5). With x-​rays, there is no equivalent “lens” to form an image, but ptychography

was implemented to allow numerical focusing from computational reconstructions of the

x-​ray diffraction pattern. These methods have now been implemented in light microscopy

systems.

In a common design, the specimen and a coherent illuminating beam are moved relative

to one another to sequentially illuminate the sample with overlapping areas (Figure 4.3b).

Another method achieves a similar effect but using a 2D array of LED light sources to sequen­

tially illuminate the sample, which circumvents the requirement for relatively slow scanning.

The diffracted light pattern is then detected by a 2D pixel photodetector array, such as simple

CCD camera. The spatial extent of this detector array can give access to a far greater region of

reciprocal (i.e., frequency) space than is available to a physical objective lens, which is limited

by its numerical aperture.

By utilizing different sequences of illumination areas, different conventional contrast

enhancement modes of light microscopy can be replicated. For example, illumination in the

center of the sample produces brightfield images, whereas illuminating the outer regions

(equivalent to obtaining data from higher diffraction angles than those in principle obtain­

able from the finite small numerical aperture of a typical objective lens) can generate equiva­

lent dark-​field images. Similarly, sequentially taking pairs of images with alternating halves of

the sample illuminated allows the reconstruction of phase contrast images. Performing a full

sequential illumination scan over the whole extent of the sample allows accurate recovery of

the phase of the wave as it travels through the specimen. This has great potential for rectifying

FIGURE 4.3  Methods to correct for image distortions and numerically refocus. (a) Uncorrected illumination (left panel)

through an optically heterogeneous sample can result in image distortion during fluorescence excitation, which can

be corrected by using adaptive optics (right panel, here shown with a deformable mirror on the excitation path, but a

similar optical component can also be placed in the imaging path for fluorescence emissions). (b) Optical ptychography

generates sample images by Fourier transforming the Fourier plane image of the sample, which permits a greater effective

numerical aperture for imaging compared to the physical objective lens and also enabling numerical refocusing of the

sample.