Abstract
An optical sensor comprises at least four detection channels, where each detection channel comprises a photodetector and a filter with a respective transmission spectrum. The transmission spectra of the at least four filters are different from one another, and the transmission spectra are set such that each of the three CIE color matching functions is a linear combination of the transmission spectra of at least two of the filters. Furthermore, a method for detecting electromagnetic radiation is provided.
Claims
1. An optical sensor operable for color measurement and spectrum reconstruction, the optical sensor comprising: at least four detection channels, where each detection channel comprises a photodetector and a filter with a respective transmission spectrum, wherein: the transmission spectra of the at least four filters are different from one another, the transmission spectra are set such that each of the three CIE color matching functions is identical to a linear combination of the transmission spectra of at least two of the filters, and the transmission spectra partially overlap with each other and are distributed over the whole visible range of the electromagnetic spectrum.
2. The optical sensor according to claim 1, wherein each transmission spectrum is assigned a scaling factor for at least one linear combination yielding one of the CIE color matching functions.
3. The optical sensor according to claim 1, wherein the wavelength of maximum transmission is at least 380 nm and at most 780 nm for each filter.
4. The optical sensor according to claim 1, wherein the wavelengths of maximum transmission of the filters are equally spaced from each other.
5. The optical sensor according to claim 4, wherein the transmission spectra of the filters are linearly independent.
6. The optical sensor according to claim 1, wherein the transmission spectra are set such that at least one transmission spectrum is employed for the linear combinations of two CIE color matching functions.
7. The optical sensor according to claim 1, wherein the filters are one of the following: interference filters, absorption filters, plasmonic filters.
8. The optical sensor according to claim 1, wherein the filters are a combination of at least two of the following: interference filters, absorption filters, plasmonic filters.
9. A method for detecting electromagnetic radiation, the method comprising: providing an optical sensor which comprises at least four detection channels, where each detection channel comprises a photodetector, providing a filter with a transmission spectrum for each detection channel, where the transmission spectra of the at least four filters are different from one another, partially overlap each other, and are distributed over the whole visible range of the electromagnetic spectrum, such that each of the three CIE color matching functions is identical to a linear combination of the transmission spectra of at least two of the filters, detecting electromagnetic radiation to be emitted from a light source with the optical sensor, where each detection channel detects a fraction of the electromagnetic radiation in a range of wavelengths that is within the transmission spectrum of the respective filter and where each detection channel provides a channel signal, determining from the channel signals a tristimulus value of the electromagnetic radiation, and reconstructing by means of suitable mathematical algorithms and/or matrix interpolation operations from the channel signals the spectrum of the electromagnetic radiation.
10. The method according to claim 9, wherein each transmission spectrum is assigned a scaling factor for at least one linear combination yielding one of the CIE color matching functions.
11. The method according to claim 10, wherein at least two channel signals are multiplied with the respective scaling factors of the transmission spectra of the filters of the respective detection channels and added to give a tristimulus value.
12. The method according to claim 9, wherein the linear combination of the transmission spectra of at least two of the filters is the sum of at least two transmission spectra that are multiplied with their respective scaling factors.
13. The method according to claim 9, wherein the channel signal of each detection channel comprises the intensity of electromagnetic radiation detected by the respective detection channel.
14. The method according to claim 9, wherein at least one channel signal is employed for determining two tristimulus values.
15. The method according to claim 9, wherein a color measurement is provided which is based on the CIE color matching functions.
16. The method according to claim 9, wherein the three tristimulus values are determined.
17. The method according to claim 9, wherein the wavelength of maximum transmission of at least one transmission spectrum is equal to the wavelength of maximum sensitivity of one of the CIE color matching functions.
18. The method according to claim 9, wherein at least two channel signals are employed for reconstructing the spectrum of the detected electromagnetic radiation.
19. The method according to claim 9, further comprising determining a remission, wherein determining the remission comprises reconstructing from at least two channel signals the spectral composition of the detected electromagnetic radiation; and determining from the spectral composition the color impression of the light source.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The following description of figures may further illustrate and explain exemplary embodiments. Components that are functionally identical or have an identical effect are denoted by identical references. Identical or effectively identical components might be described only with respect to the figures where they occur first. Their description is not necessarily repeated in successive figures.
(2) FIGS. 1A, 1B and 1C show cutaway views of exemplary embodiments of an optical sensor.
(3) In FIG. 2 the three CIE color matching functions are shown.
(4) In FIG. 3 six transmission spectra of an optical sensor are shown.
(5) In FIG. 4 the normalized CIE color matching functions are shown.
(6) In FIGS. 5A and 5B three transmission spectra of three filters are shown.
(7) In FIGS. 6A and 6B six transmission spectra are shown.
(8) In FIGS. 7A and 7B seven transmission spectra are shown.
(9) In FIGS. 8A and 8B eight transmission spectra are shown.
(10) In FIGS. 9A and 9B nine transmission spectra are shown.
(11) In FIGS. 10A and 10B ten transmission spectra are shown.
DETAILED DESCRIPTION
(12) In FIG. 1A a cutaway view of an exemplary embodiment of an optical sensor 10 is shown. The optical sensor 10 comprises four detection channels 11. Each detection channel 11 comprises a photodetector 12 and a filter 13 with a respective transmission spectrum T. The filter 13 can be for example an interference filter, an absorption filter or a plasmonic filter. The photodetectors 12 are arranged next to each other on a carrier 15. Above each photodetector 12 a filter 13 is arranged. Between the photodetectors 12 and the filters 13 other optical elements or materials can be arranged. For each detection channel 11 one filter 13 is arranged above one photodetector 12 in such a way that only electromagnetic radiation which passes the filter 13 reaches the photodetector 12.
(13) The transmission spectra T of the four filters 13 are different from one another and the transmission spectra T are set such that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13. Therefore, the tristimulus values X, Y, Z of a light source or of electromagnetic radiation detected by the optical sensor 10 can be determined. Furthermore, with the optical sensor 10 the spectral composition of a light source or of electromagnetic radiation can be analyzed.
(14) In FIG. 1B a cutaway view of a further embodiment of the optical sensor 10 is shown. The filters 13 are arranged directly above the photodetectors 12. This means, the filters 13 and the respective photodetectors 12 are in direct contact.
(15) In FIG. 1C a cutaway view of a further embodiment of the optical sensor 10 is shown. Four filters 13 are arranged on a glass plate 16. The glass plate 16 is arranged at the side of the filters 13 that faces away from the photodetectors 12. Preferably, the glass plate 16 is transparent for the electromagnetic radiation to be detected by the photodetectors 12. Between the photodetectors 12 and the filters 13 optical elements or materials can be arranged.
(16) In FIG. 2 the three CIE color matching functions x, y, z for a 10° standard observer are shown. On the x-axis the wavelength is plotted in nanometers and on the y-axis the sensitivity of the human eye is plotted in arbitrary units.
(17) The first CIE color matching function comprises two peaks in the visible range between 380 nm and 780 nm and is referred to as x or the red curve. The second CIE color matching function y comprises one peak in the visible range and is referred to as y or the green curve. The third CIE color matching function comprises one peak in the visible range and is referred to as z or the blue curve. The CIE color matching functions x, y, z describe the color sensitivity of the human eye. The sum of the CIE color matching functions x, y, z is the spectral sensitivity of the so-called standard observer.
(18) In FIG. 3 six transmission spectra T of an optical sensor are shown. On the x-axis the wavelength is plotted in nanometers and on the y-axis the transmittance is plotted in arbitrary units. For this optical sensor the six transmission spectra T are equally distributed over the visible range of the electromagnetic spectrum. In contrast, as described with the following figures, for the optical sensor 10 described here the transmission spectra T are set such that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13.
(19) In FIG. 4 the CIE color matching functions x, y, z normalized to 1 are shown. On the x-axis the wavelength is plotted in nanometers and on the y-axis the sensitivity of the human eye is plotted normalized to 1. The first CIE color matching function x is separated into two different peaks. The four peaks shown in FIG. 4 are in the following referred to as the four target functions Fx1, Fy, Fz, Fx2. The first target function Fx1, the second target function Fy, the third target function Fz and the fourth target function Fx2 represent the three CIE color matching functions x, y, z normalized to 1. According to the method described here the transmission spectra T of the at least four filters 13 are set such that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13. Therefore, the transmission spectra T of the filters 13 need to be set accordingly.
(20) In FIG. 5A the third target function Fz is plotted. Furthermore, a first transmission spectrum T1, a second transmission spectrum T2 and a third transmission spectrum T3 of three different filters 13 are plotted. On the x-axis the wavelength is plotted in nanometers and on the y-axis the transmittance is plotted normalized to 1. The x-axis and the y-axis are the same for all following figures. The three transmission spectra T1, T2, T3 are set in such a way that the sum of the three transmission spectra T1, T2, T3 gives the third target function Fz. Therefore, a linear combination of the three transmission spectra T1, T2, T3 gives the third CIE color matching function Z.
(21) The transmission spectra T1, T2, T3 are set in such a way that the wavelength of maximum transmission of the second transmission spectrum T2 is equal or approximately equal to the wavelength of maximum sensitivity of the third target function Fz. The second transmission spectrum T2 is a Gauss function. The full width at half maximum of the second transmission spectrum T2 is smaller than the full width at half maximum of the third target function Fz. The first transmission spectrum T1 and the third transmission spectrum T3 are given by the difference between the third target function Fz and the second transmission spectrum T2.
(22) In FIG. 5B the third target function Fz and the fourth target function Fx2 are plotted. Furthermore, three transmission spectra T1, T2, T3 are plotted. The sum of the second transmission spectrum T2 and the third transmission spectrum T3 gives the fourth target function Fx2. The first transmission spectrum T1 is set to be the difference between the third target function Fz and the sum of the second transmission spectrum T2 and the third transmission spectrum T3. In this way, the third CIE color matching function z is given by the sum of the three transmission spectra T1, T2, T3 and the second peak of the first CIE color matching function x, y, x is given by the sum of the second transmission spectrum T2 and the third transmission spectrum T3.
(23) With FIGS. 5A and 5B it is shown that the transmission spectra T of the at least four filters 13 are set in such a way that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of two or three filters 13. It is also possible to employ more than three transmission spectra T for a linear combination yielding a CIE color matching function.
(24) In FIG. 6A the four target functions Fx1, Fy, Fz, Fx2 and six transmission spectra T1, T2, T3, T4, T5, T6 are plotted. The sum of the first transmission spectrum T1 and the second transmission spectrum T2 gives the first target function Fx1. The sum of the second transmission spectrum T2 and the third transmission spectrum T3 gives the second target function Fy. The sum of the fourth transmission spectrum T4, the fifth transmission spectrum T5 and the sixth transmission spectrum T6 gives the third target function Fz. The sum of the fifth transmission spectrum T5 and the sixth transmission spectrum T6 gives the fourth target function Fx2.
(25) This means, the four target functions can be expressed in the following way:
Fx1=T1+T2
Fy=T2+T3
Fz=T4+T5+T6
Fx2=T5+T6
(26) In FIG. 6B the six transmission spectra T1, T2, T3, T4, T5, T6 shown in FIG. 6A are plotted normalized to 1. These six transmission spectra T1, T2, T3, T4, T5, T6 of six filters 13 are set in such a way that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13. This means, that the scaled sum of at least two of the transmission spectra T gives one of the CIE color matching functions x, y, z. Scaling factors c required for the linear combinations are determined from the summation shown in FIG. 6A. For example, the first transmission spectrum T1 and the second transmission spectrum T2 are scaled in such a way that their linear combination gives the first peak of the first CIE color matching function x. This means, the first transmission spectrum T1 is multiplied with a first scaling factor c1 and the second transmission spectrum T2 multiplied with a second scaling factor c21. The sum of the first transmission spectrum T1 multiplied with the first scaling factor c1 and the second transmission spectrum T2 multiplied with the second scaling factor c21 gives the first peak of the first CIE color matching function x.
(27) The second transmission spectrum T2 is employed for the linear combinations of two CIE color matching functions x, y, z. The sum of the second transmission spectrum T2 multiplied with a third scaling factor c22 and the third transmission spectrum T3 multiplied with a fourth scaling factor c3 gives the second CIE color matching function y. Advantageously, less detection channels 11 are required if a transmission spectrum T is employed for the linear combination of two CIE color matching functions x, y, z. Furthermore, the detection channels 11 are used in an efficient way if at least one transmission spectrum T is employed for the linear combinations of two CIE color matching functions x, y, z.
(28) Similarly, the fourth transmission spectrum T4, the fifth transmission spectrum T5 and the sixth transmission spectrum T6 are employed for the linear combination of the third CIE color matching function z. Furthermore, the fifth transmission spectrum T5 and the sixth transmission spectrum T6 are employed for the linear combination of the second peak of the first CIE color matching function x.
(29) This means, the three CIE color matching functions x, y, z can be expressed by the following linear combinations:
x=c1*T1+c21*T2+c51*T5+c61*T6
y=c22*T2+c3*T3
z=c4*T4+c52*T5+c62*T6,
(30) where c1, c21, c22, c3, c4, c51, c52, c61, c62 are the respective scaling factors.
(31) For the optical sensor 10 described here the tristimulus values X, Y, Z are determined from the signals detected by the photodetectors 12. For each linear combination the integrated signal of each photodetector 12 is multiplied with the scaling factor c of the respective filter 13. The signals of the photodetectors 12 can be for example the intensity of the detected electromagnetic radiation. For each linear combination the sum of the signals of the respective photodetectors 12 multiplied with their scaling factors c gives the respective tristimulus value X, Y, Z. With the three linear combinations the three tristimulus values X, Y, Z can be determined.
(32) Consequently, with an optical sensor 10 with filters 13 with the transmission spectra T as shown in FIG. 6B the tristimulus values X, Y, Z of light of a light source or of electromagnetic radiation can be determined. This means, the color impression for a human observer can be determined. Furthermore, the spectral composition of electromagnetic radiation detected by the optical sensor 10 can be analyzed. As the six transmission spectra T are separated from each other the six detection channels 11 can be employed for analyzing the spectral composition of electromagnetic radiation and for a reconstruction of the spectrum of the electromagnetic radiation.
(33) In FIG. 7A the four target functions and seven transmission spectra T1, T2, T3, T4, T5, T6, T7 of seven different filters 13 are plotted. The four target functions can be expressed by the seven transmission spectra T1, T2, T3, T4, T5, T6, T7 in the following way:
Fx1=T1+T2
Fy=T3+T4
Fz=T5+T6+T7
Fx2=T6+T7.
(34) The first transmission spectrum T1 and the second transmission spectrum T2 overlap with the third transmission spectrum T3 and the fourth transmission spectrum T4.
(35) In FIG. 7B the seven transmission spectra T1, T2, T3, T4, T5, T6, T7 shown in FIG. 7A are plotted normalized to 1. These seven transmission spectra T1, T2, T3, T4, T5, T6, T7 of seven filters 13 are set in such a way that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13.
(36) This means, the three CIE color matching functions x, y, z can be expressed by the following linear combinations:
x=c1*T1+c21*T2+c61*T6+c71*T7
y=c3*T3+c4*T4
z=c5*T5+c62*T6+c72*T7.
(37) In FIG. 8A the four target functions and eight transmission spectra T1, T2, T3, T4, T5, T6, T7, T8 of eight different filters 13 are plotted. The four target functions can be expressed by the eight transmission spectra T1, T2, T3, T4, T5, T6, T7, T8 in the following way:
Fx1=T1+T2+T3
Fy=T3+T4+T5
Fz=T6+T7+T8
Fx2=T6+T7+T8.
(38) In this case, the fourth target function Fx2 is approximated with the same transmission spectra T6, T7, T8 as the third target function Fz since they only slightly deviate from each other.
(39) In FIG. 8B the eight transmission spectra T1, T2, T3, T4, T5, T6, T7, T8 shown in FIG. 8A are plotted normalized to 1. These eight transmission spectra T1, T2, T3, T4, T5, T6, T7, T8 of eight filters 13 are set in such a way that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13.
(40) This means, the three CIE color matching functions x, y, z can be expressed by the following linear combinations:
x=c1*T1+c2*T2+c31*T3+c6*T6+c7*T7+c8*T8
y=c32*T3+c4*T4+c5*T5
z=c6*T6+c7*T7+c8*T8.
(41) The third transmission spectrum T3 is employed for the linear combination of the first CIE color matching function x and the second color matching function.
(42) In FIG. 9A the four target functions and nine transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9 of nine different filters 13 are plotted. The four target functions can be expressed by the nine transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9 in the following way:
Fx1=T1+T2+T3
Fy=T3+T4+T5
Fz=T6+T7+T8+T9
Fx2=T7+T8+T9.
(43) In FIG. 9B the nine transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9 shown in FIG. 9A are plotted normalized to 1. These nine transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9 of nine filters 13 are set in such a way that each of the three CIE color matching functions x, y, z is a linear combination of the transmission spectra T of at least two of the filters 13.
(44) This means, the three CIE color matching functions x, y, z can be expressed by the following linear combinations:
x=c1*T1+c2*T2+c31*T3+c71*T7+c81*T8+c91*T9
y=c32*T3+c4*T4+c5*T5
z=c6*T6+c72*T7+c82*T8+c92*T9.
(45) In FIG. 10A the four target functions and ten transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9, T10 of ten different filters 13 are plotted. The four target functions can be expressed by the ten transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9, T10 in the following way:
Fx1=T1+T2+T3
Fy=T4+T5+T6
Fz=T7+T8+T9+T10
Fx2=T8+T9+T10
(46) In FIG. 10B the ten transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9, T10 shown in FIG. 10A are plotted normalized to 1. These ten transmission spectra T1, T2, T3, T4, T5, T6, T7, T8, T9, T10 of ten filters 13 are set in such a way that each of the three CIE color matching functions y, z is a linear combination of the transmission spectra T of at least two of the filters 13.
(47) This means, the three CIE color matching functions x, y, z can be expressed by the following linear combinations:
x=c1*T1+c2*T2+c3*T3+c81*T8+c91*T9+c101*T10
y=c4*T4+c5*T5+c6*T6
z=c7*T7+c82*T8+c92*T9+c102*T10.
(48) With an increasing number of detection channels 11 of the optical sensor 10 the spectral resolution of the optical sensor 10 increases.
