Apparatus and methods for measuring the optical thickness and index of refraction of thin, optical membranes

Claim 1

A method comprising directing light onto a thin, optical membrane at one or more known angles of incidence, said membrane having a thickness in the range of about 0.5 to about 10 micrometers, said membrane being capable of being edge-supported; finding two consecutive null angles of incidence for said membrane; calculating the thickness t of said membrane from the expression: t√(sin I2) 2 -(sin I1) 2 =(λ/2)√k-1, where I2 and I1, are said two consecutive null angles of incidence for said membrane, λ is the wavelength of the incident light, and k is an assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane; then calculating the index of refraction N of said membrane from the calculated value of t and the assumed value of k in the expression: Nt=k(λ/4), where N is equal to the square root of the expression N 2 -(sin I) 2 , I is I1 or I2, and N is the index of refraction for said membrane.

Claim 2

A method comprising directing light onto a thin, optical membrane at one or more known angles of incidence, said membrane having a thickness in the range of about 0.5 to about 10 micrometers, said membrane being capable of being edge-supported; finding two consecutive null angles of incidence for said membrane; calculating the thickness t of said membrane from the expression: t√(sin I2) 2 -(sin I1) 2 =(λ/2)√k-1, where I2 and I1, are said two consecutive null angles of incidence for said membrane, λ is the wavelength of the incident light, and k is an assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane; then calculating the index of refraction N of said membrane from the calculated value of t and the assumed value of k in the expression: Nt=k(λ/4), where N is equal to the square root of the expression N 2 -(sin I) 2 , I is I1 or I2, and N is the index of refraction for said membrane.

Claim 3

A method comprising directing light onto a thin, optical membrane at one or more known angles of incidence, said membrane having a thickness in the range of about 0.5 to about 10 micrometers, said membrane being capable of being edge-supported; finding two consecutive null angles of incidence for said membrane; calculating the thickness t of said membrane from the expression: t√(sin I2) 2 -(sin I1) 2 =(λ/2)√k-1, where I2 and I1 are said two consecutive null angles of incidence for said membrane, λ is the wavelength of the incident light, and k is an assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane; then calculating the index of refraction N of said membrane from the calculated value of t and the assumed value of k in the expression Nt=k(λ/4), where N is equal to the square root of the expression N 2 -(sin I) 2 , I is I1 or I2 and N is the index of refraction for said membrane; then directing light onto another thin, optical membrane having a thickness in the range of about 0.5 to about 10 micrometers, and being capable of being edge-supported, at a null angle of incidence for said other membrane; and then calculating the thickness t of said other membrane from the expression Nt=kλ/4 where λ is the wavelength of the incident light; k is said assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane; N is equal to the square root of the expression N 2 -(sin I) 2 ; and N is said calculated value of the index of refraction of said membrane, and most closely approximates the nominal value of the index of refraction for said membrane.

Claim 4

A method comprising directing light onto a thin, optical membrane at one or more known angles of incidence, said membrane having a thickness in the range of about 0.5 to about 10 micrometers, said membrane being capable of being edge-supported; finding two consecutive null angles of incidence for said membrane; calculating the thickness t of said membrane from the expression: t√(sin I2) 2 -(sin I1) 2 =(λ/2)√k-1, where I2 and I1 are said two consecutive null angles of incidence for said membrane, λ is the wavelength of the incident light, and k is an assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane; then calculating the index of refraction N of said membrane from the calculated value of t and the assumed value of k in the expression Nt=k(λ/4), where N is equal to the square root of the expression N 2 -(sin I) 2 , I is I1 or I2 and N is the index of refraction for said membrane; then directing light onto another thin, optical membrane having a thickness in the range of about 0.5 to about 10 micrometers, and being capable of being edge-supported, at a null angle of incidence for said other membrane; and then calculating the thickness t of said other membrane from the expression Nt=kλ/4 where λ is the wavelength of the incident light; k is said assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane; N is equal to the square root of the expression N 2 -(sin I) 2 ; and N is said calculated value of the index of refraction of said membrane, and most closely approximates the nominal value of the index of refraction for said membrane.

Claim 5

A method comprising directing light onto a thin, optical membrane at one or more known angles of incidence, said membrane having a thickness in the range of about 0.5 to about 10 micrometers, said membrane being capable of being edge-supported; finding two consecutive null angles of incidence for said membrane; calculating the thickness t of said membrane from the expression: t√(sin I2) 2 -(sin I1) 2 =(λ/2)√k-1, where I2 and I1 are said two consecutive null angles of incidence for said membrane, λ is the wavelength of the incident light, and k is an assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane s; then calculating the index of refraction N of said membrane from the calculated value of t and the assumed value of k in the expression Nt=k(λ/4), where N is equal to the square root of the expression N 2 -(sin I) 2 , I is I1 or I2, and N is the index of refraction for said membrane; then directing light onto another thin, optical membrane having a thickness in the range of about 0.5 to about 10 micrometers and being capable of being edge-supported; finding two consecutive null angles of incidence for said other membrane; computing the thickness t of said other membrane from the expression (N3-N4)t=λ/2 where N3=√N 2 -(sin I3) 2 ; and N4=√N 2 -(sin I4) 2 ; I3 is the first null angle of incidence for said other membrane; I4 is the second null angle for said other membrane; λ is the wavelength of the incident light striking said other membrane; and N is said calculated value of the index of refraction of said membrane and most closely approximates the nominal value of the index of refraction for said membrane.

Claim 6

A method comprising directing light onto a thin, optical membrane at one or more known angles of incidence, said membrane having a thickness in the range of about 0.5 to about 10 micrometers, said membrane being capable of being edge-supported; finding two consecutive null angles of incidence for said membrane; calculating the thickness t of said membrane from the expression: t√(sin I2) 2 -(sin I1) 2 =(λ/2)√k-1, where I2 and I1 are said two consecutive null angles of incidence for said membrane, λ is the wavelength of the incident light, and k is an assumed, even integer value, in quarter wavelengths of light, for the optical thickness of said membrane s; then calculating the index of refraction N of said membrane from the calculated value of t and the assumed value of k in the expression Nt=k(λ/4), where N is equal to the square root of the expression N 2 -(sin I) 2 , I is I1 or I2, and N is the index of refraction for said membrane; then directing light onto another thin, optical membrane having a thickness in the range of about 0.5 to about 10 micrometers and being capable of being edge-supported; finding two consecutive null angles of incidence for said other membrane; computing the thickness t of said other membrane from the expression (N3-N4)t=λ/2 where N3=√N 2 -(sin I3) 2 ; and N4=√N 2 -(sin I4) 2 ; I3 is the first null angle of incidence for said other membrane; I4 is the second null angle for said other membrane; λ is the wavelength of the incident light striking said other membrane; and N is said calculated value of the index of refraction of said membrane and most closely approximates the nominal value of the index of refraction for said membrane.