Asian Journal of Physics Vol 30, No 1  (2021) 31-43

Resolving power of optical instruments: A Tutorial*

Rajpal Sirohi
Alabama A&M University, Huntsville AL 35802
Dedicated to Professor M S Sodha for his numerous contributions to
Plasma Physics, Optics and Photonics, Energy Studies and Education Management


Optical instruments are used for observation and spectroscopy apart from host of many other applications. Both in observation and spectroscopy it is important to know how closely two objects, or two spectral lines can be resolved by the instruments. There had been a number of criteria of resolution: two most often used are Rayleigh criterion and Sparrow criterion. Rayleigh criterion of resolution has no mathematical support but is often used due to its simplicity. Sparrow criterion gives the lowest limit of resolution. Further in seeing, the nature of illumination of the object has profound effect on the limit of resolution. Rayleigh criterion tacitfully assumes incoherent illumination, while the Sparrow criterion can be applied to incoherent, partially coherent and coherent illuminations. Applicability of Rayleigh criterion can be extended to partially coherent and incoherent illuminations by a simple modification. The paper through the tutorial approach describes the resolution of optical instruments used for seeing and spectroscopy. © Anita Publications. All rights reserved.
Keywords: Resolution, Telescope, Microscope, Fabry-Perot, Grating, Resolving Power

DOI: 10.54955.AJP.30.1.2021.31-43


Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

  1. Sodha M S, Resolving power of Fabry Perot Etalon, Curr Sci, 22(1953)139-140.
  2. Sodha M S, Effect of absorption by material of prism on its resolving power, Am J Phys, 21(1953)313; doi. 10.1119 /1.1933431.
  3. Sodha M S, Agrawal A K, On limit of resolution of telescope, Optik, 24(1966)189-196.
  4. Sodha M S, Agrawal A K, Resolution of objects of unequal intensity in an annular aperture telescope, Optik, 24(1966)197-200.
  5. Sodha M S, Resolving power of an instrument with circular aperture in white light, Optik, 16(1959)276.
  6. Katti P K, Singh K, Resolving Power of the Fabry-Perot Interferometer and the Reflection Echelon Used for Visual Observations of Absorption Spectra, Appl Opt, 6(1967)1134-1136.
  7. Sparrow C M, On Spectroscopic Resolving Power, Astrophys J, 44(1916)76-86.
  8. Asakura T, On the Sparrow Resolution Criterion, Oyo Buturi, 31(1962)709-715.
  9. Barakat Richard, Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. I. Coherent Illumination, J Opt Soc Am, 52(1962)276-283.
  10. Grimes D N, Thompson B J, Two-Point Resolution with Partially Coherent Light, J Opt Soc Am, 57(1967)1330-1334.
  11. Falconi Oscar, Limits to which Double Lines, Double Stars, and Disks can be Resolved and Measured, J Opt Soc Am, 57(1967)987-993.
  12. Young M, Faulkner B, Cole J, Resolution in Optical Systems Using Coherent Illumination, J Opt Soc Am, 60(1970)137-138.
  13. Sirohi R S, Bhatnagar G S, Effect of partial coherence on the resolution of a microscope, Optica Acta, 17(1970) 839-842.
  14. Bhatnagar G S, Sirohi R S, Sharma, S K, Two point resolution in partially coherent light, Opt Commun, 3(1971) 269-271.
  15. Nayyar V P, Verma N K, Two-point resolution of Gaussian aperture operating in partially coherent light using various resolution criteria, Appl Opt, 17(1978)2176-2180.
  16. Asakura T, Resolution of two unequally bright points with partially coherent light, Nouv Rev Opt, 5(1974)169-177.
  17. Asakura T, Ueno T, Apodization for increasing two-point resolution by the sparrow criterion under the partially coherent illumination, Nouv Rev Opt, 5(1974)349-359.
  18. den Dekker A J, van den Bos A, Resolution: a survey, J Opt Soc Am,17(1997)547-555.
  19. Heintzmann R, Sarafis V, Two point resolution in incoherent imaging, Optik, 112(2001)114-118.
  20. Reddy A N K, Sagar D K, Two-point resolution of asymmetrically apodized optical systems, Opt Pura Apl, 46 (2013)215-222.
  21. Reddy A N K, Khonina S N, Apodization for improving the two-point resolution of coherent optical systems with defect of focus, Appl Phys B, 124(2018)229; doi.org/10.1007/s00340-018-7101-z.
  22. Cremer C, Masters B R, Resolution enhancement techniques in microscopy, Eur Phys J H, 38(2013)281-344.
  23. Lord Rayleigh, Investigations in optics, with special reference to the spectroscope, Philosophical Magazine, Ser V, 8(1879)261-274.
  24. Lord Rayleigh, On the resolving power of telescopes, Philosophical Magazine, 10(1880)116-119.
  25. Dawes W R, Catalogue of micrometrical measurements of double stars, Mem Roy Astron Soc, 35(1867)137-502.
  26. Schuster A, Theory of Optics, (E Arnold & Co, London, UK), 1924.
  27. Houston W, A compound interferometer for fine structure work, Phys Rev, 29(1927)478-484.
  28. Buxton A, Note on optical resolution, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 23(1937)440-442.
  29. Born M, Wolf E, The Principles of Optics, 4th edn, (Pergamon Press), 1970, pp 419-424.
  30. Harris J L, Resolving power and decision theory, J Opt Soc Am, 54(1964)606-611.
  31. Toraldo di Francia G, Resolving power and information, J Opt Soc Am, 45(1955)497-501.
  32. McCutchen C W, Super resolution in microscopy and the Abbe resolution limit, J Opt Soc Am, 57(1967)1190-1192.
  33. Lukosz W, Optical systems with resolving powers exceeding the classical limit: I, J Opt Soc Am, 56(1966)1463-1472.
  34. Lukosz W, Optical systems with resolving powers exceeding the classical limit: II, J Opt Soc Am, 57(1967)932-941.
  35. Treanor P J, On the telescopic resolution of unequal binaries, The Observatory, 66(1946)255-258
  36. Mahapatra D P, Mattoo S K, Exact evaluation of the transmitted amplitude for a Fabry-Perot interferometer with surface defects, Appl Opt, 25(1986)1646-1649.
  37. Palik E D, Boukari H, Gammon R W, Experimental study of the effect of surface defects on the finesse and contrast of a Fabry–Perot interferometer, Appl Opt, 35(1996)38-50.