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CRC Press eBooks

Observation and Information

Francis T.S. Yu, Francis T.S. Yu

Published Oct 8, 2018• 0 citations
Publisher

Abstract

In the classical theory of light, an observation can be made as small as we please. However, for some very small objects this assumption does not hold true. For example, let us take a Mach-Zehnder interferometer [1], as shown in Fig. 6.1. It can be seen that only a very small fraction of light is required to illuminate the object transparency s(x, y). This small fraction of light, however, carries all the information that we intended. However, the other path of light carries almost all the energy of the light source. The corresponding irradiance distributed on the photographic emulsion is [2] /(/?, q) = R2 + \S(p, q)\2 + 2RS(p, q)cos[oc0p + >(/?, q)] (6.1) where R is the background (reference) beam, S(p, q) is the corresponding Fourier spectrum of the object transparency, (/?, q) are the corresponding spatial frequency coordinates, ao is an arbitrary constant, and S(p, q) = \S(p, q)\ exp [/>(/>, q)] (6.2) In our example, it is assumed that R » \S(p, q)\. Thus the interference term (the last term) is considered very small in comparison with the background irradiance. In principle, it is possible to enhance the weak interference term by means of a coherent optical processor [2], so it is simply a matter of making s(x, y) observable. In the classical theory, it is possible to observe with as weak an object beam as we wish. However, we know instinctively that this is not practical, since an increase in background light would at the same time increase background fluctuation. Thus the informational term (the interference term), could be completely buried in the background fluctuation. So in practice there exists a practical lower limit. Beyond this limit it is not possible to retrieve the information (the object).

DOI
10.1201/9781315214498-12

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In the classical theory of light, an observation can be made as small as we please. However, for some very small objects this assumption does not hold true. For example, let us take a Mach-Zehnder interferometer [1], as shown in Fig. 6.1. It can be seen that only a very small fraction of light is required to illuminate the object transparency s(x, y). This small fraction of light, however, carries all the information that we intended. However, the other path of light carries almost all the energy of the light source. The corresponding irradiance distributed on the photographic emulsion is [2] /(/?, q) = R2 + \S(p, q)\2 + 2RS(p, q)cos[oc0p + >(/?, q)] (6.1) where R is the background (reference) beam, S(p, q) is the corresponding Fourier spectrum of the object transparency, (/?, q) are the corresponding spatial frequency coordinates, ao is an arbitrary constant, and S(p, q) = \S(p, q)\ exp [/>(/>, q)] (6.2) In our example, it is assumed that R » \S(p, q). Thus the interference term (the last term) is considered very small in comparison with the background irradiance. In principle, it is possible to enhance the weak interference term by means of a coherent optical processor [2], so it is simply a matter of making s(x, y) observable. In the classical theory, it is possible to observe with as weak an object beam as we wish. However, we know instinctively that this is not practical, since an increase in background light would at the same time increase background fluctuation. Thus the informational term (the interference term), could be completely buried in the background fluctuation. So in practice there exists a practical lower limit. Beyond this limit it is not possible to retrieve the information (the object).
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