Posted by Alejandro Cornejo-Rodríguez, OSA Fellow, and Fermín Granados-Agustín

In the field of interferometry, there is a well-known classification between wavefront division interferometers and amplitude division interferometers.¹ Some examples of wavefront division interferometers are the Young’s experiment, Fresnel’s prism and lens, Billet’s lens, Lloyd’s mirror, the stellar Michelson’s interferometer and the Chalmer scheme.² On the other hand, for the case of the amplitude division interferometers, examples include the classical arrangements devised by Newton, Fizeau, Mach-Zender, Jamin, Lummer and Gehrke, and Michelson.³  

Of course, there are many different types of modifications to these interferometers that have appeared over the years in the literature.^4,5,6 Some other books describe the various experimental schemes for different applications, taking into account, among other characteristics, equal or unequal paths of the interfering wavefronts; the use of white or different light sources, or different kinds of lasers; the traveling of different or common paths of the interfering beams; or according to the kind of interference fringes that are observed.  

However, an interesting interferometer that cannot be easily classified in one of the well-known categories is the one invented by Linnik⁷ and used many years later by Smartt and Strong and Smartt and Steel⁸—the so-called point diffraction interferometer. The plate used for producing the interference between two wavefronts contains a small open pinhole on a glass plate that produces the reference W_r by wavefront division.  

On the other hand, the other wavefront, the one to be analyzed, is passing through the rest of the plate with a reduced transmission by amplitude division. Hence, it seems that this kind of interferometer has classical characteristics for producing interference phenomena, while at the same time it acts as an interferometer with wavefront and amplitude divisions. 

Some other interferometric arrangements used for optical testing are the Ronchi and Hartmann tests, both of which have been classified as interferometric methods.⁹ In the case of the Ronchi test, the set-up is considered as a lateral shearing interferometer.¹⁰ However, it is also a wavefront division device and not just an amplitude division interferometer, from the point of view of a lateral shear interferometer.  

In the same sense, the Hartmann scheme is a wavefront division interferometer, with information in two perpendicular directions, and the Ronchi test only in one. In the case of the Ronchi test, if a phase grating is used, as in the case of the Linnik interferometer, an amplitude division interferometer is working with the use of the Ronchi grating; but at the same time, as a wavefront division instrument. 

Another set-up that works as a wavefront division system is the Shack-Hartmann technique used in adaptive optics systems.¹¹ However, if somehow a phase shift is introduced between its apertures, the method can be classified as an experimental arrangement working with a wavelength or amplitude division interferometer. There is a particular scheme in which a reflective diffraction grating is used for producing interference,¹² where the first orders are used for observing the interference fringes. Once more, if the diffraction grating is converted in a phase grating, the interference pattern observed is due to the combination of wavefronts produced by the interferometer. 

In view of the previous analysis, it can be considered that between the classical classification of interferometers by wavefront and amplitude divisions, there is a third class of interferometric schemes that use both interference methods, at the same time, for producing interference fringes. 

The authors would like to thank John N. Howard, the editor of OPN’s history column, for his enlightening comments on this manuscript.  

[Alejandro Cornejo-Rodríguez and Fermín Granados-Agustín are with the Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Puebla Pue, México.] 

References
1. F. Jenkins  and H. White. “The principles of Optics,” Mc Graw Hill Co., 1932.
2. S.D. Chalmers. “The Testing of Photographic Lenses,” Transaction Opt. Soc. 5, 87 (1903).
3. M. Born  and E. Wolf. “Principles of Optics”. 7^th (expanded) edition, Cambridge, University Press, 1999.
4. W.H. Steel. “Interferometry,” Cambridge University Press, 1967.
5. F. Twyman. “Prism and Lens Making”, Hilger and Watts, London, Chapters 11 and 12 (1957).
6. D. Malacara, ed. “Optical Shop Testing.” 3^rd edition, John Wiley & Sons (2007, Anniversary).
7. W. Linnik. “Simple Interferometer to Test Optical Systems,” Comptes Rendus de l’Academie des Science d l’URSS 1, 208 (1933). Abstract in Z. Instrumentenkd 54, 463 (1934).
8. R.N. Smartt and J. Strong. “Point Diffraction Interferometer” (abstract only), J. Opt. Soc. Am. 62, 737 (1972). R.N. Smartt and W.H. Steel. “Theory and application point diffraction interferometer,” Proceedings of the ICO Conference on Optical Methods, in Scientific and Industrial Measurements Tokyo, 1974. Jap. J. Appl. Phys., 14, Suppl. 1, 351 (1975).
9. A. Cordero-Dávila et al. “Ronchi and Hartmann Tests With Same Mathematical Theory,” Appl. Opt. 31, 2370-6 (1992).
10. V. Ronchi. “Sur la Nature Interferentielle des Frangesd’Ombre dans l’Essai des Sistems Optiques,” Rev. Opt. 5, 441 (1926).
11. R.V. Shack and B.C. Platt. “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (abstract only), 1971.
12. C.K. Munnerlyn et al. “Interferometric Measurement of Optically Rough Surfaces,” IEEE J. Quantum Electron., QE-5, 359 (1969). 

2007-12 December, Miscellaneous Optics interferometry, instrumentation