Method and apparatus to determine spatial distribution of magnitude and phase of electro-magnetic fields especially optical fields

Claim 1

A method of numerically determining the distribution of magnitude and phase of a time harmonic electromagnetic, particularly an optical, wave field comprising: a. engendering a reference wave field such that its spatial distribution is similar to the field to be measured whereby fringes are obtained the position of which varies slowly with the recording coordinates; b. using the reference wave as reference surface; c. recording under far field conditions point by point by means of photodetector three interference fringe patterns which belong to the unknown field and variations of the said reference field distribution, the relationship of said variations as to magnitude and phase being such as to uniquely determine, for any recording point, the amplitude and phase distribution of the unknown electromagnetic wave field; d. recording data in numeral form obtained from the photodetector; e. placing an optical element in the said reference wave optical path such that the reference wave front is shifted in relation to the unknown wave front by a small known amount; f. repeating the measurements as in (c) and (d); and g. processing said data to obtain numeral values of magnitude and phase of the electromagnetic wave field being measured, such as to provide information in terms of a smooth spherical wavefront.

Claim 2

A method of numerically determining the distribution of magnitude and phase of a time harmonic electromagnetic, particularly an optical, wave field comprising: a. engendering a reference wave field such that its spatial distribution is similar to the field to be measured whereby fringes are obtained the position of which varies slowly with the recording coordinates; b. using the reference wave as reference surface; c. recording under far field conditions point by point by means of photodetector three interference fringe patterns which belong to the unknown field and variations of the said reference field distribution, the relationship of said variations as to magnitude and phase being such as to uniquely determine, for any recording point, the amplitude and phase distribution of the unknown electromagnetic wave field; d. recording data in numeral form obtained from the photodetector; e. placing an optical element in the said reference wave optical path such that the reference wave front is shifted in relation to the unknown wave front by a small known amount; f. repeating the measurements as in (c) and (d); and g. processing said data to obtain numeral values of magnitude and phase of the electromagnetic wave field being measured, such as to provide information in terms of a smooth spherical wavefront.

Claim 7

A method of numerically determining the distribution of magnitude and phase of an unknown time harmonic electro-magnetic, particularly an optical wave field comprising: a. engendering a reference electromagnetic wave field such that its spatial distribution is similar to the wave field to be measured, whereby on interference between the unknown and reference wave fields, fringes are obtained the position of which varies slowly with the recording coordinates; b. using the wavefront of the reference wave as a reference of the field to be measured in particular the reference field being such that its spatial distribution is similar to the field to be measured, whereby the ratio of the complex-valued amplitude of object field and reference field depends weakly on the spatial coordinates and consequently the recording coordinates may be known only within limits large compared to the wavelength of the light; c. recording point by point by means of a photodetector three or more interference fringe patterns which belong to the unknown field and variations of said reference field distributions, the relationship of said variations being such that for any recording point the complex-valued amplitude R l of the lth variation, l = 1,2,3, . . . satisfies the relation R.sub.l = (δ.sub.l R)R where R is some arbitrary complex number and where real and imaginary parts of the complex numbers δ l R = δ l R r jδ l R i are known and satisfy the condition (δ.sub.1 R.sub.r -δ.sub.2 R.sub.r) (δ.sub.2 R.sub.i -δ.sub.3 R.sub.i) - (δ.sub.2 R.sub.r -δ.sub.3 R.sub.r) (δ.sub.1 R.sub.i -δ.sub.2 R.sub.i) ≠ 0 d. solving by means of a computer the simultaneous system of equations ##EQU38## for α r and α i at every recording point with given data of J 1 , J 2 , J 3 , . . . of the irradiance and with known values of |R| 2 , δ l R r , and δ l R i , l = 1,2,3, . . . , and where Ε r , α i are real and imaginary part, respectively, of the ratio of the complex-valued amplitude of the field to be measured and the reference field at the recording point; e. placing an optical element in the said reference wave optical path such that the reference wave front is shifted in relation to the unknown wave front by a small known amount; f. repeating the steps of (c) and (d) such that the method is carried out twice with one object field of arbitrary spatial distribution but two variations of the reference field such that the complex-valued amplitude of the 1st reference field at the (k 1)th recording point (R 1 (k 1)) and the complex-valued amplitude of the second reference field at the kth recording point (R 2 (k)) satisfy the relation R.sub.1 (k+1) = f(k) R.sub.2 (k), where f(k) is a known complex number and whereby the complex-valued amplitude of the 1st reference field R 1 at the kth recording point can be derived (except some irrelevant constant (R 1 1 ) from the expression R.sub.1 (k) = μ(1) μ(2) . . . μ(k-1) f(1)f(2) . . . f(k-1) R.sub.1.sup.1 where the complex number μ(k) is the ratio of the measurable quantities α 1 (k) and α 2 (k) obtained at the kth recording point with the said two variations of the reference field, ##EQU39## and g. processing said data to obtain numeral values of magnitude and phase of the electromagnetic wave field being measured, said data being sufficient to eliminate the reference wave information from the obtained information which can be related to a mathematically exact wavefront.

Claim 8

A method of numerically determining the distribution of magnitude and phase of an unknown time harmonic electro-magnetic, particularly an optical wave field comprising: a. engendering a reference electromagnetic wave field such that its spatial distribution is similar to the wave field to be measured, whereby on interference between the unknown and reference wave fields, fringes are obtained the position of which varies slowly with the recording coordinates; b. using the wavefront of the reference wave as a reference of the field to be measured in particular the reference field being such that its spatial distribution is similar to the field to be measured, whereby the ratio of the complex-valued amplitude of object field and reference field depends weakly on the spatial coordinates and consequently the recording coordinates may be known only within limits large compared to the wavelength of the light; c. recording point by point by means of a photodetector three or more interference fringe patterns which belong to the unknown field and variations of said reference field distributions, the relationship of said variations being such that for any recording point the complex-valued amplitude R l of the lth variation, l = 1,2,3, . . . satisfies the relation R.sub.l = (δ.sub.l R)R where R is some arbitrary complex number and where real and imaginary parts of the complex numbers δ l R = δ l R r jδ l R i are known and satisfy the condition (δ.sub.1 R.sub.r -δ.sub.2 R.sub.r) (δ.sub.2 R.sub.i -δ.sub.3 R.sub.i) - (δ.sub.2 R.sub.r -δ.sub.3 R.sub.r) (δ.sub.1 R.sub.i -δ.sub.2 R.sub.i) ≠ 0 d. solving by means of a computer the simultaneous system of equations ##EQU38## for α r and α i at every recording point with given data of J 1 , J 2 , J 3 , . . . of the irradiance and with known values of |R| 2 , δ l R r , and δ l R i , l = 1,2,3, . . . , and where Ε r , α i are real and imaginary part, respectively, of the ratio of the complex-valued amplitude of the field to be measured and the reference field at the recording point; e. placing an optical element in the said reference wave optical path such that the reference wave front is shifted in relation to the unknown wave front by a small known amount; f. repeating the steps of (c) and (d) such that the method is carried out twice with one object field of arbitrary spatial distribution but two variations of the reference field such that the complex-valued amplitude of the 1st reference field at the (k 1)th recording point (R 1 (k 1)) and the complex-valued amplitude of the second reference field at the kth recording point (R 2 (k)) satisfy the relation R.sub.1 (k+1) = f(k) R.sub.2 (k), where f(k) is a known complex number and whereby the complex-valued amplitude of the 1st reference field R 1 at the kth recording point can be derived (except some irrelevant constant (R 1 1 ) from the expression R.sub.1 (k) = μ(1) μ(2) . . . μ(k-1) f(1)f(2) . . . f(k-1) R.sub.1.sup.1 where the complex number μ(k) is the ratio of the measurable quantities α 1 (k) and α 2 (k) obtained at the kth recording point with the said two variations of the reference field, ##EQU39## and g. processing said data to obtain numeral values of magnitude and phase of the electromagnetic wave field being measured, said data being sufficient to eliminate the reference wave information from the obtained information which can be related to a mathematically exact wavefront.