Point diffraction interferometer

A point diffraction interferometer (PDI) is a type of common path interferometer. Unlike an amplitude splitting interferometer, such as a Michelson, which separates out an unaberrated beam and interferes this with the test beam, a common path interferometer generates its own reference beam. In PDI systems, the test and reference beams travel the same or almost the same path. This design makes the PDI extremely useful when environmental isolation is not possible or a reduction in the number of precision optics is required. The reference beam is created from a portion of the test beam by diffraction from a small pinhole in a semitransparent coating. The principle of a PDI is shown in Figure 1. 

Figure 1: Basic layout of a PDI system, where the reference beam is generated by a pinhole etched onto a semi transparent film.

The device is similar to a spatial filter. Incident light is focused onto a semi-transparent mask (about 0.1% transmission). In the centre of the mask there is a hole about the size of the Airy disc and the beam is focused onto this hole with a Fourier transforming lens. The zeroth order (the low frequencies in Fourier space) then passes through the hole and interferes with the rest of beam. The transmission and the hole size are selected to balance the intensities of the test and reference beams. The device is similar in operation to Zernike phase contrast microscopy.

Development in PDI systems

Figure 2: Fizeau interferometer requires a reference optics. It is very important that the reference optics(flat) be near perfect because it heavily influence the measured surface form of a test object.

PDI systems are valuable tool to measure absolute surface characteristics of an optical or reflective instruments non destructively. The common path design eliminates any need of having a reference optics, which are known to overlap the absolute surface form of a test object with its own surface form errors. This is a major disadvantage of a double path systems, such as Fizeau interferometers, as shown in Figure 2. Similarly the common path design is resistant to ambient disturbances. The main criticisms of the original design are (1) that the required low-transmission reduces the efficiency, and (2) when the beam becomes too aberrated, the intensity on-axis is reduced, and less light is available for the reference beam, leading to a loss of fringe contrast. Lowered transmission was associated with lowered signal to noise ratio. These problems are largely overcome in the phase-shifting point diffraction interferometer designs, in which a grating or beamsplitter creates multiple, identical copies of the beam that is incident on an opaque mask. The test beam passes through a somewhat large hole or aperture in the membrane, without losses due to absorption; the reference beam is focused onto the pinhole for highest transmission. In the grating-based instance, phase-shifting is accomplished by translating the grating perpendicular to the rulings, while multiple images are recorded. The continued developments in phase shifting PDI have achieved accuracy orders of magnitude greater than standard Fizeau based systems.

Types of PDI systems

Sommargren scheme

Gary Sommargren proposed a point diffraction interferometer design which directly followed from the basic design where parts of the diffracted wavefront was used for testing and the remaining part for detection as shown in Figure 3. This design was a major upgrade to existing systems. The scheme could accurately measure the optical surface with variations of 1 nm. The phase shifting was obtained by moving the test part with piezo electric translation stage.

Since the device is self-referencing it can be used in environments with a lot of vibrations or when no reference beam is available such as in many adaptive optics and short-wavelength scenarios.

Phase-shifting [see Interferometry] versions have been created to increase measurement resolution and efficiency. These include a diffraction grating interferometer by Kwon and the Phase-Shifting Point Diffraction Interferometer.

The main criticisms of the original design are (1) that the required low-transmission reduces the efficiency, and (2) when the beam becomes too aberrated, the intensity on-axis is reduced, and less light is available for the reference beam, leading to a loss of fringe contrast. These problems are largely overcome in the phase-shifting point diffraction interferometer design, in which a grating or beamsplitter creates multiple, identical copies of the beam that is incident on an opaque mask. The test beam passes through a somewhat large hole or aperture in the membrane, without losses due to absorption; the reference beam is focused onto the pinhole for highest transmission. In the grating-based instance, phase-shifting is accomplished by translating the grating perpendicular to the rulings, while multiple images are recorded.