Patent ID: 8447546

Claim:
A measurement method of Fourier coefficients using an integrating photometric detector, comprising: measuring a number of exposures (S j ) of light with a predetermined integration time during a predetermined time period using the integrating photometric detector; and determining Fourier coefficients for a waveform of an intensity of the light by carrying out a discrete Fourier transform with respect to the number of measured exposures (S j ) wherein the number of exposures (S j ) are measured using the integrating photometric detector with a read time (T r ) as follows: S j = ∫ ( j - 1 ) ⁢ T / M + T r ( j - 1 ) ⁢ T / M + T r + T int ⁢ I ′ ⁡ ( t ) ⁢ ⁢ ⅆ t , ⁢ ( j = 1 , 2 , 3 , Λ , M ) , with a predetermined integration time (T int ) for a time period (T) and then, from the number of measured exposures (S j ), the normalized Fourier coefficients (α′ 2n ,β′ 2n ) for the waveform of the light intensity are determined respectively as follows: α 2 ⁢ n ′ = ξ 2 ⁢ n ⁢ csc ⁡ ( ξ 2 ⁢ n ) ⁢ { a 2 ⁢ n ⁢ cos ⁡ [ ξ 2 ⁢ n ⁡ ( 1 + 2 ⁢ T r T int ) ] - b 2 ⁢ n ⁢ sin ⁡ [ ξ 2 ⁢ n ⁡ ( 1 + 2 ⁢ T r T int ) ] } , ⁢ β 2 ⁢ n ′ = ξ 2 ⁢ n ⁢ csc ⁡ ( ξ 2 ⁢ n ) ⁢ { a 2 ⁢ n ⁢ sin ⁡ [ ξ 2 ⁢ n ⁡ ( 1 + 2 ⁢ T r T int ) ] + b 2 ⁢ n ⁢ cos ⁡ [ ξ 2 ⁢ n ⁡ ( 1 + 2 ⁢ T r T int ) ] } , {T: period, M: number of measuring the exposure with the predetermined time interval during the period T, T r : read time, T int : integration time, I ′ ⁡ ( t ) = I 0 ′ ⁢ { 1 + ∑ n = 1 N ⁢ [ α 2 ⁢ n ′ ⁢ cos ⁡ ( 4 ⁢ π ⁢ ⁢ n ⁢ ⁢ t / T ) + β 2 ⁢ n ′ ⁢ sin ⁡ ( 4 ⁢ π ⁢ ⁢ n ⁢ ⁢ t / T ) ] } , I′(t): light intensity, I′ 0 : mean value of the light intensity, α′ 2n and β′ 2n : normalized Fourier coefficients, 2N : natural number that indicates the highest order of the normalized Fourier coefficients other than 0, ξ n = n ⁢ ⁢ π ⁢ ⁢ T int T , ⁢ a 2 ⁢ n = 2 Md 0 ⁢ ∑ j = 1 M ⁢ S j ⁢ cos ⁡ [ 4 ⁢ n ⁢ ⁢ π ⁡ ( j - 1 ) M ] , ⁢ b 2 ⁢ n = 2 Md 0 ⁢ ∑ j = 1 M ⁢ S j ⁢ sin ⁡ [ 4 ⁢ n ⁢ ⁢ π ⁡ ( j - 1 ) M ] , ⁢ d 0 = 1 M ⁢ ∑ j = 1 M ⁢ S j } .