Point diffraction interferometer

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Figure 1: Basic layout of a PDI system, where the reference beam is generated by a pinhole etched onto a semitransparent film Common path PDI.png
Figure 1: Basic layout of a PDI system, where the reference beam is generated by a pinhole etched onto a semitransparent film

A point diffraction interferometer (PDI) [1] [2] [3] is a type of common-path interferometer. Unlike an amplitude-splitting interferometer, such as a Michelson interferometer, 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. [4] [5] The principle of a PDI is shown in Figure 1.

Contents

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 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 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. Fizeau interferometer testing optical flat.svg
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. [4]

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. [6]

Phase-shifting [see Interferometry] versions have been created to increase measurement resolution and efficiency. These include a diffraction grating interferometer by Kwon [7] and the Phase-Shifting Point Diffraction Interferometer. [5] [6] [8] [9]

Types of phase-shifting PDI systems

Phase-shifting PDI with single pinhole

Figure 3: Phase-shifting point diffraction interferometer design proposed by Gary Sommargren Phase shifting Point diffraction interferometer Sommargren.png
Figure 3: Phase-shifting point diffraction interferometer design proposed by Gary Sommargren

Gary Sommargren [11] 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 a piezo electric translation stage. [12] [13] An unwanted side effect of moving the test part is that the defocus also moves distorting the fringes. Another downsides of Sommargren's approach is that it produces low contrast fringes [14] and an attempt to regulate the contrast also modifies the measured wavefront.

PDI systems using optical fibres

In this type of point diffraction interferometer the point source is a single mode fiber. The end face is narrowed down to resemble a cone and is covered with metallic film to reduce the light spill. Fibre is arranged so that they generate spherical waves for both testing and referencing. End of an optical fibre is known to generate spherical waves with an accuracy greater than . [15] Although optical fibre based PDIs provide some advancement over the single pinhole based system, they are difficult to manufacture and align.

Figure 4: Two-beam phase-shifting point diffraction interferometer, where the reference beam can be independently regulated for phase shifting and contrast regulation Two beam phase shifting point diffraction interferometer updated.png
Figure 4: Two-beam phase-shifting point diffraction interferometer, where the reference beam can be independently regulated for phase shifting and contrast regulation

Two-beam phase-shifting PDI

Two-beam PDI provides a major advantage over other schemes by availing two independently steerable beams. Here, the test beam and reference beam are perpendicular to each other, where the intensity of reference can be regulated. Similarly, an arbitrary and stable phase shifts can be obtained relative to the test beam keeping the test part static. The scheme as shown in Figure 4 is easy to manufacture and provides user-friendly measuring conditions similar to Fizeau type interferometers. At the same time renders following additional benefits:

  1. Absolute surface form of the test part.
  2. High numerical aperture (NA = 0.55).
  3. Clear fringe patterns of high contrast.
  4. High accuracy of surface form testing (wavefront RMS error 0.125 nm).
  5. Simple RMS repeatability 0.05 nm.
  6. Can measure depolarising test parts.

The device is self-referencing, therefore 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.

Absolute surface form obtained by phase-shifting interferometry using an industrial point diffraction interferometer manufactured by Difrotec Absolute surface form of a lens measured by Difrotec's D7.png
Absolute surface form obtained by phase-shifting interferometry using an industrial point diffraction interferometer manufactured by Difrotec

Applications of PDI

Interferometry has been used for various quantitative characterisation of optical systems indicating their overall performance. Traditionally, Fizeau interferometers have been used to detect optical or polished surface forms but new advances in precision manufacturing has allowed industrial point diffraction interferometry possible. PDI is especially suited for high resolution, high accuracy measurements in laboratory conditions to noisy factory floors. Lack of reference optics makes the method suitable to visualise absolute surface form of optical systems. Therefore, a PDI is uniquely suitable to verify the reference optics of other interferometers. It is also immensely useful in analysing optical assemblies used in Laser based systems. Characterising optics for UV lithography. Quality control of precision optics. Verifying the actual resolution of an optical assembly. Measuring the wavefront map produced by X-ray optics. PS-PDI can also be used to verify rated resolution of space optics before deployment.

See also

Related Research Articles

<span class="mw-page-title-main">Diffraction grating</span> Optical component which splits light into several beams

In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions. The emerging coloration is a form of structural coloration. The directions or diffraction angles of these beams depend on the wave (light) incident angle to the diffraction grating, the spacing or periodic distance between adjacent diffracting elements on the grating, and the wavelength of the incident light. The grating acts as a dispersive element. Because of this, diffraction gratings are commonly used in monochromators and spectrometers, but other applications are also possible such as optical encoders for high-precision motion control and wavefront measurement.

<span class="mw-page-title-main">Interferometry</span> Measurement method using interference of waves

Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.

<span class="mw-page-title-main">Mach–Zehnder interferometer</span> Device to determine relative phase shift

The Mach–Zehnder interferometer is a device used to determine the relative phase shift variations between two collimated beams derived by splitting light from a single source. The interferometer has been used, among other things, to measure phase shifts between the two beams caused by a sample or a change in length of one of the paths. The apparatus is named after the physicists Ludwig Mach and Ludwig Zehnder; Zehnder's proposal in an 1891 article was refined by Mach in an 1892 article. Mach–Zehnder interferometry with electrons as well as with light has been demonstrated. The versatility of the Mach–Zehnder configuration has led to its being used in a range of research topics efforts especially in fundamental quantum mechanics.

<span class="mw-page-title-main">Michelson interferometer</span> Common configuration for optical interferometry

The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.

<span class="mw-page-title-main">Wavefront</span> Locus of points at equal phase in a wave

In physics, the wavefront of a time-varying wave field is the set (locus) of all points having the same phase. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency.

<span class="mw-page-title-main">Neutron interferometer</span> Interferometer using neutron diffraction to make precise measurements

In physics, a neutron interferometer is an interferometer capable of diffracting neutrons, allowing the wave-like nature of neutrons, and other related phenomena, to be explored.

<span class="mw-page-title-main">Shearing interferometer</span>

The shearing interferometer is an extremely simple means to observe interference and to use this phenomenon to test the collimation of light beams, especially from laser sources which have a coherence length which is usually significantly longer than the thickness of the shear plate so that the basic condition for interference is fulfilled.

In optics, in particular scalar diffraction theory, the Fresnel number, named after the physicist Augustin-Jean Fresnel, is a dimensionless number relating to the pattern a beam of light forms on a surface when projected through an aperture.

)|Humphrey Lloyd]] in the Transactions of the Royal Irish Academy. Its original goal was to provide further evidence for the wave nature of light, beyond those provided by Thomas Young and Augustin-Jean Fresnel. In the experiment, light from a monochromatic slit source reflects from a glass surface at a small angle and appears to come from a virtual source as a result. The reflected light interferes with the direct light from the source, forming interference fringes. It is the optical wave analogue to a sea interferometer.

Holographic interferometry (HI) is a technique which enables the measurements of static and dynamic displacements of objects with optically rough surfaces at optical interferometric precision. These measurements can be applied to stress, strain and vibration analysis, as well as to non-destructive testing and radiation dosimetry. It can also be used to detect optical path length variations in transparent media, which enables, for example, fluid flow to be visualised and analyzed. It can also be used to generate contours representing the form of the surface.

Digital holography is the acquisition and processing of holograms with a digital sensor array, typically a CCD camera or a similar device. Image rendering, or reconstruction of object data is performed numerically from digitized interferograms. Digital holography offers a means of measuring optical phase data and typically delivers three-dimensional surface or optical thickness images. Several recording and processing schemes have been developed to assess optical wave characteristics such as amplitude, phase, and polarization state, which make digital holography a very powerful method for metrology applications .

<span class="mw-page-title-main">Fizeau interferometer</span>

A Fizeau interferometer is an interferometric arrangement whereby two reflecting surfaces are placed facing each other. As seen in Fig 1, the rear-surface reflected light from the transparent first reflector is combined with front-surface reflected light from the second reflector to form interference fringes.

<span class="mw-page-title-main">Talbot effect</span> Near-field diffraction effect

The Talbot effect is a diffraction effect first observed in 1836 by Henry Fox Talbot. When a plane wave is incident upon a periodic diffraction grating, the image of the grating is repeated at regular distances away from the grating plane. The regular distance is called the Talbot length, and the repeated images are called self images or Talbot images. Furthermore, at half the Talbot length, a self-image also occurs, but phase-shifted by half a period. At smaller regular fractions of the Talbot length, sub-images can also be observed. At one quarter of the Talbot length, the self-image is halved in size, and appears with half the period of the grating. At one eighth of the Talbot length, the period and size of the images is halved again, and so forth creating a fractal pattern of sub images with ever-decreasing size, often referred to as a Talbot carpet. Talbot cavities are used for coherent beam combination of laser sets.

A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.

<span class="mw-page-title-main">Phase-contrast X-ray imaging</span> Imaging systems using changes in phase

Phase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography (CT) rely on a decrease of the X-ray beam's intensity (attenuation) when traversing the sample, which can be measured directly with the assistance of an X-ray detector. However, in phase contrast X-ray imaging, the beam's phase shift caused by the sample is not measured directly, but is transformed into variations in intensity, which then can be recorded by the detector.

<span class="mw-page-title-main">White light interferometry</span> Measurement technique

As described here, white light interferometry is a non-contact optical method for surface height measurement on 3D structures with surface profiles varying between tens of nanometers and a few centimeters. It is often used as an alternative name for coherence scanning interferometry in the context of areal surface topography instrumentation that relies on spectrally-broadband, visible-wavelength light.

Single-shot multi-contrast x-ray imaging is an efficient and a robust x-ray imaging technique which is used to obtain three different and complementary types of information, i.e. absorption, scattering, and phase contrast from a single exposure of x-rays on a detector subsequently utilizing Fourier analysis/technique. Absorption is mainly due to the attenuation and Compton scattering from the object, while phase contrast corresponds to phase shift of x-rays.

<span class="mw-page-title-main">Virtually imaged phased array</span> Dispersive optical device

A virtually imaged phased array (VIPA) is an angular dispersive device that, like a prism or a diffraction grating, splits light into its spectral components. The device works almost independently of polarization. In contrast to prisms or regular diffraction gratings, the VIPA has a much higher angular dispersion but has a smaller free spectral range. This aspect is similar to that of an Echelle grating, since it also uses high diffraction orders. To overcome this disadvantage, the VIPA can be combined with a diffraction grating. The VIPA is a compact spectral disperser with high wavelength resolving power.

Grating-coupled interferometry (GCI) is a biophysical characterization method mainly used in biochemistry and drug discovery for label-free analysis of molecular interactions. Similar to other optical methods such as surface plasmon resonance (SPR) or bio-layer interferometry (BLI), it is based on measuring refractive index changes within an evanescent field near a sensor surface. After immobilizing a target to the sensor surface, analyte molecules in solution which bind to that target cause a small increase in local refractive index. By monitoring these refractive changes over time characteristics such as kinetic rates and affinity constants of the analyte-target binding, or analyte concentrations, can be determined.

References

  1. ↑ Linnik, W. P. (1933). "A Simple Interferometer for the Investigation of Optical Systems". C. R. Acad. Sci. URSS. 5: 210.
  2. ↑ Smartt, R. N.; W. H. Steel (1975). "Theory and application of Point-Diffraction interferometers". Japanese Journal of Applied Physics. 14 (S1): 351–356. Bibcode:1975JJAPS..14..351S. doi:10.7567/jjaps.14s1.351. S2CID   121804757.
  3. ↑ Smartt, R. N.; Strong, J. (1972). "Point-Diffraction Interferometer". Journal of the Optical Society of America. 62: 737. Bibcode:1974JOSA...62..737S.
  4. 1 2 Neal, Robert M.; Wyant, James C. (2006-05-20). "Polarization phase-shifting point-diffraction interferometer". Applied Optics. 45 (15): 3463–3476. Bibcode:2006ApOpt..45.3463N. doi:10.1364/AO.45.003463. hdl: 10150/280372 . ISSN   1539-4522. PMID   16708090.
  5. 1 2 Voznesenskiy, Nikolay; Voznesenskaia, Mariia; Petrova, Natalia; Abels, Artur (2012-12-18). Mazuray, Laurent; Wartmann, Rolf; Wood, Andrew P; de la Fuente, Marta C; Tissot, Jean-Luc M; Raynor, Jeffrey M; Kidger, Tina E; David, Stuart; Benítez, Pablo; Smith, Daniel G; Wyrowski, Frank; Erdmann, Andreas (eds.). "Alignment of phase-shifting interferograms in the two-beam point diffraction interferometer". Optical Systems Design 2012. 8550. International Society for Optics and Photonics: 85500R–85500R–8. doi:10.1117/12.980910. S2CID   123535031.{{cite journal}}: Cite journal requires |journal= (help)
  6. 1 2 "Product — Difrotec". difrotec.com. Retrieved 2017-03-20.
  7. ↑ Kwon, Osuk (February 1984). "Multichannel phase-shifted interferometer". Optics Letters. 9 (2): 59–61. Bibcode:1984OptL....9...59K. doi:10.1364/ol.9.000059. PMID   19718235.
  8. ↑ Medecki, Hector (1996). "A Phase-Shifting Point Diffraction Interferometer". Optics Letters. 21 (19): 1526–1528. Bibcode:1996OptL...21.1526M. doi:10.1364/OL.21.001526. PMID   19881713.
  9. ↑ Naulleau, Patrick (1999). "Extreme-ultraviolet phase-shifting point-diffraction interferometer: a wave-front metrology tool with subangstrom reference-wave accuracy". Applied Optics. 38 (35): 7252–7263. Bibcode:1999ApOpt..38.7252N. doi:10.1364/ao.38.007252. PMID   18324274.
  10. ↑ Otaki, Katsura; Bonneau, Florian; Ichihara, Yutaka (1999-01-01). "Absolute measurement of a spherical surface using a point diffraction interferometer". Optical Engineering for Sensing and Nanotechnology (ICOSN '99). 3740: 602–605. Bibcode:1999SPIE.3740..602O. doi:10.1117/12.347755. S2CID   119631152.{{cite journal}}: Cite journal requires |journal= (help)
  11. ↑ "Interferometer". str.llnl.gov. Retrieved 2017-03-20.
  12. ↑ G. E. Sommargren, U.S. Patent No. 554840 1996 .
  13. ↑ Rhee, Hyug-Gyo; Kim, Seung-Woo (2002-10-01). "Absolute distance measurement by two-point-diffraction interferometry". Applied Optics. 41 (28): 5921–5928. Bibcode:2002ApOpt..41.5921R. doi:10.1364/AO.41.005921. ISSN   1539-4522. PMID   12371550.
  14. ↑ Voznesenskiy, Nikolay; Voznesenskaia, Mariia; Petrova, Natalia; Abels, Artur (2013-05-13). "Concept, realization and performance of a two-beam phase-shifting point diffraction interferometer". In Lehmann, Peter H; Osten, Wolfgang; Albertazzi, Armando (eds.). Optical Measurement Systems for Industrial Inspection VIII. Vol. 8788. International Society for Optics and Photonics. pp. 878805–878805–13. doi:10.1117/12.2020618. S2CID   109782639.
  15. ↑ Chkhalo, Nikolay I.; Kluenkov, Evgeniy B.; Pestov, Aleksey E.; Raskin, Denis G.; Salashchenko, Nikolay N.; Toropov, Mikhail N. (2008-01-01). "Manufacturing and investigation of objective lens for ultrahigh resolution lithography facilities". Micro- and Nanoelectronics 2007. SPIE Proceedings. 7025: 702505–702505–6. Bibcode:2008SPIE.7025E..05C. doi:10.1117/12.802351. S2CID   55343344.
  16. ↑ "Difrotec D7 is a high accuracy industrial point diffraction interferometer". www.difrotec.com. Retrieved 2017-04-28.
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