Apparatus for measuring optical information in scattering medium and method therefor

Modulated light from a light source is incident on the surface of a scattering medium, and light passing through this scattering medium is externally detected. Components having a plurality of angular frequencies .omega..sub.1 and .omega..sub.2 corresponding to photon density waves propagating in the scattering medium are extracted from this detection signal. The extracted signals corresponding to these waves are compared with a signal of original modulated light to be incident on the scattering medium to detect a quantitatively measurable predetermined parameter such as a phase difference at a detection point for each angular frequency. The detected predetermined parameters have a predetermined relationship with absorptive and scattering constituents of the scattering medium. A pair of predetermined parameters are appropriately arithmetically calculated to eliminate the scattering coefficient, so that only the absorption coefficient can be independently calculated. Various pieces of information (including the linear integration value of the absorption coefficient in the scattering medium, the concentration of the specific material in the scattering medium, and the like) associated with absorption and the like in the scattering medium can be obtained in accordance with the calculated absorption coefficient.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to absolute-value measurement of optical 
information associated with scattering and absorptive constituents in a 
scattering medium by utilizing modulated light and, more particularly, to 
an apparatus for measuring optical information in the scattering medium, 
capable of measuring an equivalent scattering coefficient, an absorption 
coefficient, and the concentration of a specific constituent in the 
scattering medium, their time rate changes, spatial distributions, and the 
like, and improving measurement precision, and a method therefor. 
2. Related Background Art 
Light does not propagate straight in a scattering medium because the light 
is scattered and absorbed at random. The total amount of light is not 
reduced in a scattering medium whose absorption is zero. However, light 
propagates in the medium at random in a zig-zag manner because the light 
is scattered by the scattering constituent at random. In this case, an 
average optical pathlength through which light propagates without the 
influence of scattering is a reciprocal number of an equivalent scattering 
coefficient (to be described later). This reciprocal number is called a 
mean free path or mean diffusion length. This pathlength in a biological 
sample is about 2 mm. However, as an absorptive constituent is contained 
in addition to the scattering constituent in a scattering medium, random 
absorption occurs to attenuate light in accordance with the light 
propagation path length. 
A well-known Lambert-Beer law is valid in the above scattering medium. 
According to this law, the absorbance or optical density of the scattering 
medium is proportional to the product of the molar absorption coefficients 
and the molar concentrations of the constituents and thickness of the 
scattering medium. This law is regarded as a basic principle in absorbance 
analysis. 
In the absorbance measuring method, the attenuation coefficient by its 
definition is a sum of an equivalent scattering coefficient and an 
absorption coefficient. These scattering and absorption coefficients are 
processed as equivalent parameters. For this reason, it is impossible to 
separate influences of scattering and absorption and to accurately measure 
the influence of absorption, e.g., the absorption coefficient. To overcome 
this, the principle of two-wavelength spectroscopy is generally applied to 
this absorbance measuring method. More specifically, at least two 
appropriate light beams having different wavelengths and different 
absorption coefficients with respect to an absorptive constituent are used 
to measure the absorbance values. 
In this case, it is assumed that the scattering coefficients or equivalent 
scattering coefficients at these at least two wavelengths are identical to 
each other or have a very small difference, if any. The influence of 
scattering is eliminated in accordance with the difference between the 
absorbance values derived from these at least two light beams, thereby 
obtaining the absorption coefficient or the concentration of the 
absorptive constituent. 
According to this method, as can be apparent from the above measurement 
principle, a large error occurs due to the assumption that the scattering 
coefficients are equal to each other with respect to the light components 
having different wavelengths. In addition, the influence of scattering, 
i.e., the scattering coefficient itself cannot be measured. As techniques 
similar to this, a method of measuring an absorbance difference using two- 
or three-wavelength continuous, pulsed, or modulated light and a method 
using the above principle of two-wavelength spectroscopy in addition to 
the above method of measuring the absorbance difference are also 
available. These methods also have the same disadvantage as that of the 
above principle, and this disadvantage cannot be eliminated. 
Strong demand has conventionally arisen for measurements of absorptive 
constituents in scattering media such as living bodies or improvements of 
measurement accuracy, and various efforts and attempts have been made. 
Major efforts and attempts are summarized as references.sup.1)-7) at the 
end of this section. 
In these references, a common problem, i.e., a problem encountered upon 
application of the principle of two-wavelength spectroscopy to absorbance 
measurements including scattering, is posed. In addition, the following 
problems are also posed. In the following description, .sup.x) represents 
the reference number. 
Tamura et al..sup.1) proposed the measuring principle of an oxyhemoglobin 
concentration and a reduced or deoxygenated hemoglobin concentration in 
accordance with a change of absorbance optical density with respect to 
incident light components having three different wavelengths. Optical CT 
construction using this principle is also attempted. However, this method 
has the above problem and poses another problem in which a measurement 
error is increased by the way of handling an optical pathlength upon a 
change in absorption coefficient in absorbance measurement. 
References.sup.2-4) are attempts for time-resolved measurement where 
time-resolved output signal with respect to the incidence of pulsed light 
is used to measure internal absorption information. At this time, an 
output light signal upon incidence of the pulsed light on a scattering 
medium is a light signal output which has a wide time width caused by 
scattering and absorption and a long, gradually attenuated tail. 
Patterson et al..sup.2) assumed a model of a uniform scattering medium to 
analytically obtain a light signal output in response to pulsed light 
incidence. A waveform representing a time change in intensity of the 
optical signal given by the formula defined by Patterson et al. matches a 
waveform obtained by an experiment using a uniform scattering medium. 
According to them, the absorption coefficient of an absorptive constituent 
constituting the scattering medium is given by a slope (differential 
value) obtained when the optical signal is sufficiently attenuated, i.e., 
when a sufficiently long period elapses. 
According to this method, however, since the optical signal corresponding 
to a portion subjected to absorption coefficient measurement must be 
sufficiently attenuated, the S/N ratio of the signal becomes low, and an 
error increases. It is difficult to use this method in practice. In 
addition, a long period of time must elapse until the optical signal 
output is sufficiently attenuated, and the measurement time is inevitably 
prolonged. 
To the contrary, Chance et al..sup.3) proposed a method.sup.3) of obtaining 
a slope at an earlier timing (when the light intensity is not sufficiently 
attenuated) to approximate an absorption coefficient with the slope value. 
According to their report, an error in a simple scattering medium such as 
a uniform medium is about 10%. However, there is no guarantee that the 
above waveform is monotonously attenuated in an actual living body having 
a complicated structure, and an error caused by an increase in DC light 
component is further added. In the above three references, the scattering 
coefficient cannot be measured. 
Sevick, Chance, et al.sup.4) calculated an average optical pathlength of 
detected output light components from the barycenter, i.e., the average 
delay time of the waveform of an output signal obtained by Patterson et 
al. mentioned above, and confirmed dependency of the average optical 
pathlength on the absorption coefficient. They also attempted to measure 
an absorptive constituent localized inside the scattering medium from a 
change in average optical pathlength.sup.4). 
The method of Sevick, Chance, et al. explicitly suggests that application 
of the concept of the average optical pathlength which depends on 
absorption allows measurement of absorption information in the scattering 
medium. However, the above average delay time can be obtained only after 
the output signal waveform becomes apparent as a whole. For this reason, 
measurement of the average delay time must be delayed until the output 
light signal having a long, gradually attenuated tail is sufficiently 
attenuated, thereby prolonging the measurement time. 
According to this method, since the output light signal is obtained by 
time-resolved measurement, the improvement of measurement precision of 
time to improve measurement precision of the average optical pathlength 
undesirably causes a decrease in S/N ratio. Therefore, the measurement 
precision has a limitation. Signal processing for obtaining the barycenter 
is complicated, and an apparatus for performing time-resolved measurement 
is generally complicated and bulky, resulting in an impractical 
application. 
On the other hand, Gratton et al. proposed a method.sup.5) utilizing light 
modulated with a sinusoidal wave in imaging of the interior of a 
scattering medium. This method utilizes coherent propagation of a photon 
density wave having a modulated frequency component in the scattering 
medium, as will be described in detail with reference to the operational 
principle of the present invention. 
According to their report.sup.5), although a coherent photon density wave 
propagating in the scattering medium is confirmed in their experiment, 
optical parameters of a sample actually used in the experiment do not 
match the theoretically calculated values. This study is still in the 
stage of fundamental study. No detailed findings and means have been 
obtained for a method of calculating absorption and scattering 
coefficients as one of the objects of the present invention, a method of 
obtaining the concentration of a specific constituent, and the like. 
Chance proposed a method and apparatus for determining the concentration of 
an absorptive constituent in a scattering medium utilizing modulated light 
in 1989 prior to the report of Gratton et al., and U.S. Pat. No. 
4,972,331.sup.6) of this method was issued to Chance in 1990. According to 
the basic principle of this patent, an output signal upon incidence of 
modulated light on the scattering medium is detected and compared with a 
reference waveform (incident light waveform) to determine a quantitatively 
measurable parameter, an optical pathlength obtained in the time-resolved 
measurement mentioned earlier is calculated, and the concentration of the 
absorptive constituent is quantitatively measured. 
This patent also discloses an application of the two-wavelength 
spectroscopy principle. This reference, however, uses two wavelengths to 
eliminate the influence of scattering. That is, Chance's patent proposes a 
technique for accurately measuring the optical pathlengths in accordance 
with a phase difference method. The Chance's patent is substantially 
identical to the conventional techniques described above and cannot 
eliminate the conventional drawback. That is, a scattering coefficient and 
a measurement error caused by a scattering coefficient difference in an 
application of the two-wavelength spectroscopy cannot be measured. 
In addition, Chance also mentions that the phase difference obtained by the 
method of this patent is equal to the optical pathlength (barycenter of 
the wave) obtained in the time-resolved measurement and that logarithmic 
conversion of this phase difference is proportional to the concentration 
of the absorptive constituent of a scattering medium. The latter fact, 
however, is greatly different from the analytic and experimental results 
of the present invention, as will be described in detail later. The 
present invention does not require the determination of the optical 
pathlength. That is, the optical pathlength need not be calculated or 
measured. 
In recent years, Sevick, Chance, et al..sup.7) systematically examined and 
analyzed the relationship between various parameters obtained in the 
time-resolved measurement method and a method (they call this method a 
frequency-resolved measurement method) utilizing the modulated light, 
including the analysis results of researchers except for Sevick, Chance, 
et al., and conducted experiments to verify their analysis results.sup.7). 
Most of the major conventional methods for measuring absorption 
information in a scattering medium are examined in this report, which is 
very convenient for us. The relationship between the parameters obtained 
by the time-resolved and frequency-resolved measurement methods is 
clarified. For example, when the modulation frequency is low, the phase 
difference obtained by the frequency-resolved measurement method is found 
to be proportional to the average optical pathlength obtained by the 
time-resolved measurement method. This is partially disclosed in the 
Chance's patent described above. 
The report by Sevick, Chance, et al. describes detailed applications of the 
time-resolved measurement method which they have been studying. For 
example, the following method is described in detail. That is, parameters 
such as an average optical pathlength and an absorption coefficient are 
obtained from an output light signal obtained by the time-resolved 
measurement method. By using these parameters, the concentration and 
absorption coefficient of the absorptive constituent, the degree of 
saturation of hemoglobin (concentration of oxyhemoglobin with respect to 
the total amount of oxyhemoglobin and reduced hemoglobin), and the like in 
the scattering medium are obtained. These measurements employ the 
above-mentioned principle of two-wavelength spectroscopy, resulting in 
errors caused by the scattering coefficient differences. As described 
above, there are no new findings in this report, but this report can serve 
as a reference for understanding their idea. 
Finally, to clarify the foundation of the present invention, differences 
between the present invention and the Chance's patent.sup.6) "Phase 
Modulated Spectroscopy" will be briefly described below. It is pointed out 
that, in the Chance's patent, although two-wavelength spectroscopy has 
various advantages in detection of changes in hemoglobin and cytochrome in 
a living tissue, as described in the part of the "background of the 
invention", the basic problem of a method of this type lies in that an 
animal model which allows elimination of hemoglobin to allow direct 
measurement of cytochrome must be referred to calculate the optical 
pathlength of a living body as an object to be measured because the 
optical pathlength is unknown. 
It is then stated that a possible application of this method is a clinical 
study of time-resolved spectroscopy (TRS) using a picosecond optical pulse 
capable of quantitatively measuring a change in hemoglobin concentration 
upon determination of the optical pathlength and determining the actual 
concentrations of hemoglobin and cytochrome. In addition, it is suggested 
that when this time-resolved spectroscopy and continuous wave spectroscopy 
(CWS) are used together, the optical pathlength of photon migration can be 
calibrated to widen the application field according to Chance's patent. 
The above descriptions are assumed to indicate the importance of Chance's 
patent. 
In contrast to a measurement algorithm closely associated with the above 
optical pathlength, the present invention utilizes a new measurement 
algorithm using a function having a form excluding the optical pathlength 
or a form excluding the optical pathlength as a variable. The optical 
pathlength naturally need not be calculated. In Chance's patent, the 
difference between the scattering coefficients with respect to different 
wavelengths causes a measurement error. To the contrary, according to the 
present invention, the influence of scattering can be eliminated because 
waves having at least two different frequency components are used in 
calculating optical information associated with absorption. The optical 
information associated with absorption can be accurately measured. That 
is, by using the waves having two different frequencies, the influence of 
scattering can be perfectly eliminated according to the present invention. 
The first part of the "summary of the invention" of the specification of 
the Chance's patent describes that "when the carrier frequency is selected 
so that its time characteristics match the delay time of the photon 
migration during the period between the input to the scattering medium and 
the output therefrom, it is found that the principle of two-wavelength 
spectroscopy can be applied to time-resolved spectroscopic measurement". 
According to a description in the second half of the description of the 
third embodiment, since a carrier wave having a high frequency of 220 MHz 
is used in the apparatus of Chance's invention, measurement accuracy of 
the photon migration time between the input and the output of the 
characteristic time measured to be about 5 ns can be greatly improved. 
The sensitivity of the disclosed apparatus is indicated to be about 
70.degree./ns and 3.degree./cm of the change in optical pathlength. To 
apply the principle of two-wavelength spectroscopic measurement to the 
time-resolved spectroscopic measurement, the value of the carrier 
frequency must be selected such that the time characteristics of the 
carrier wave match the delay time between the input and output in photon 
migration. 
According to a description in the second half of the last paragraph in the 
part of the detailed description, as the great advantage of the phase 
modulated spectroscopy, i.e., the method of his patent, it is emphasized 
that the optical pathlength can be obtained without any assumption. 
According to this description, when the optical output is exponentially 
attenuated and the photon migration length is large, the phase modulated 
spectroscopy can provide a function of emphasizing the delay time of about 
5 ns, and his method is one of the most convenient embodiments of the 
time-resolved spectroscopic measurement. 
Judging from the above description, Chance's patent is based on the 
findings obtained in the time-resolved spectroscopic measurement. The 
optical pathlength is determined by the phase modulated spectroscopy. At 
this time, the time characteristic, i.e., the period of the carrier wave 
is set almost equal to the delay time of photon migration, thereby 
apparently improving measurement accuracy of the delay time, i.e., the 
optical pathlength. 
In other words, in the Chance's patent, a method of applying the principle 
of two-wavelength spectroscopic measurement to the time-resolved 
spectroscopic measurement is very effective. However, since determination 
or measurement of the optical pathlength by the time-resolved 
spectroscopic measurement is greatly limited due to the time resolution as 
the performance of the apparatus, complexity of the apparatus, high cost, 
and the like, the optical pathlength is measured by a simple phase 
difference method. 
To the contrary, as described above, the present invention is based on a 
measurement method based on the entirely new concept and principle which 
are different from a conventional time-resolved spectroscopic measurement 
including the one disclosed in the Chance's patent or the combination of 
the time-resolved spectroscopic measurement and the two-wavelength 
spectroscopic measurement. 
The optical pathlength measured in Chance's patent need not be measured in 
the present invention because the present invention is not based on the 
principle of time-resolved spectroscopic measurement. The present 
invention does not require selection of the frequency of a carrier wave 
required in the Chance's patent (according to the present invention, the 
carrier wave is expressed as a predetermined frequency component 
constituting modulated light), i.e., the present invention need not 
satisfy the condition that "the carrier frequency is selected so that its 
time characteristics match the delay time of the photon migration during 
the period between the input to the scattering medium and the output 
therefrom". 
The present invention does not have any limitation concerning frequencies 
in principle. The principle of two-wavelength spectroscopic measurement 
can be applied in the entire frequency range. In this case, the difference 
between the scattering coefficients for different wavelengths need not be 
considered. That is, the present invention uses photon density waves 
having at least two different frequencies to eliminate the influence of 
scattering, as compared with the Chance's patent using two different 
wavelengths. 
The differences between the present invention and the prior art have been 
clarified, and the inventive step, effectiveness, and importance of the 
present invention will be readily understood. 
REFERENCES 
1) I. Oda, Y. Ito, H. Eda, T. Tamura, T. Takada, R. Abumi, K. Nagai, H. 
Nakagawa, and M. Tamura: Non-invasive hemoglobin oxygenation monitor and 
computed tomography by NIR spectrophotometry, Proc. SPIE, Vol. 1431, pp. 
284-293 (1991) 
2) M. S. Patterson, J. D. Moulton, B. C. Wilson, and B. Chance: Application 
of time-resolved light scattering measurements to photodynamic theraphy 
dosimetry, Proc. SPIE, Vol. 1203, pp. 62-75 (1990) 
3) M. S. Patterson, B. Chance, and B. C. Wilson: Time resolved reflectance 
and transmittance for the non-invasive measurement of tissue optical 
properties, Applied Optics, Vol. 28, No. 12, pp. 2331-2336 (1989) 
4) E. M. Sevick, N. G. Wang, and B. Chance: Time-dependent photon imaging, 
Proc. SPIE, Vol 1599, pp. 273-283 (1991) 
5) J. Fishkin, E. Gratton, M. J. vande Ven, and W. W. Mantulin: Diffusion 
of intensity modulated near-infrared light in turbid media, Proc. SPIE, 
Vol. 1431, pp. 122-135 (1991) 
6) U.S. Pat. No. 4,972,331 (the corresponding Japanese patent is Japanese 
Patent Laid-Open No. 2-234048) 
7) E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris: Quantitation 
of time and frequency-resolved optical spectra for determination of tissue 
oxygenation, Anal. Biochem., Vol. 195, pp. 330-351 (1991) 
SUMMARY OF THE INVENTION 
In order to solve the above problems, an apparatus for measuring optical 
information in a scattering medium comprises (a) light-emitting means for 
emitting modulated light of a predetermined wavelength, (b) light-incident 
means for causing the modulated light of the predetermined wavelength to 
be incident on the scattering medium, (c) photodetecting means for 
photodetecting the modulated light, changed during propagation in the 
scattering medium, through an aperture located near an outer surface of 
the scattering medium, (d) signal extracting means for extracting a signal 
of a predetermined frequency component constituting the modulated light 
from signals photodetected by the photodetecting means, (e) parameter 
detecting means for comparing the signal extracted by the signal 
extracting means with the signal of the predetermined frequency component 
of the modulated light to be incident on the scattering medium and 
detecting a predetermined parameter associated with propagation of a 
photon density wave having the predetermined frequency component in the 
scattering medium and scattering and absorption of the light of the 
predetermined wavelength constituting the photon density wave having the 
predetermined frequency component in the scattering medium, and (f) 
arithmetic processing means for calculating optical information associated 
with the absorption of the scattering medium in accordance with a given 
relationship between the plurality of predetermined parameters 
respectively corresponding to signals having at least two predetermined 
frequency components, and the scattering and absorption for the light of 
the predetermined wavelength during propagating of the photon density wave 
having the predetermined frequency component in the scattering medium, 
using a relationship obtained by eliminating an influence of scattering 
from the given relationship. 
According to the present invention, a method of measuring optical 
information in a scattering medium comprises (a) the first step of 
emitting modulated light of a predetermined wavelength, (b) the second 
step of causing the modulated light of the predetermined wavelength to be 
incident on the scattering medium, (c) the third step of photodetecting 
the modulated light, changed during propagation in the scattering medium, 
through an aperture located near an outer surface of the scattering 
medium, (d) the fourth step of extracting a signal of a predetermined 
frequency component constituting the modulated light from signals 
photodetected in the third step, (e) the fifth step of comparing the 
signal extracted in the fourth step with the signal of the predetermined 
frequency component of the modulated light to be incident on the 
scattering medium and detecting a predetermined parameter associated with 
propagation of a photon density wave having the predetermined frequency 
component in the scattering medium and scattering and absorption of the 
light of the predetermined wavelength constituting the photon density wave 
having the predetermined frequency component in the scattering medium, and 
(f) the sixth step of calculating optical information associated with the 
absorption of the scattering medium in accordance with a given 
relationship between the plurality of predetermined parameters 
respectively corresponding to signals having at least two predetermined 
frequency components, and the scattering and absorption for the light of 
the predetermined wavelength during propagating of the photon density wave 
having the predetermined frequency component in the scattering medium, 
using a relationship obtained by eliminating an influence of scattering 
from the given relationship. 
According to the apparatus for measuring optical information of a 
scattering medium and a method therefor of the present invention, when 
modulated light is incident on the scattering medium, the photon density 
wave having the predetermined frequency component constituting the 
modulated light is attenuated. Assuming that the modulated light 
coherently and regularly propagates the scattering medium, a plurality of 
quantitatively measurable parameters respectively corresponding to the 
waves having at least two different predetermined frequency components 
modified by the scattering and absorptive constituents in the scattering 
medium are arithmetically processed. 
That is, a relationship from which the influence of scattering is 
eliminated using the given relationship between the plurality of 
parameters and the scattering and absorption of the scattering medium can 
be derived, and optical information associated with the absorption is 
calculated from the resultant relationship using the plurality of 
parameters. Optical information associated with scattering can also be 
calculated, as needed. 
The apparatus and method of the present invention will be described in more 
detail. In the apparatus and method of the present invention, a signal of 
output light is optically detected by a photodetector or the like having 
an aperture located on a side opposite to a modulated light source located 
near the surface of, e.g., a scattering medium. The signal having the 
predetermined frequency component is extracted from the output light 
signal to detect the photon density wave propagating through the 
scattering medium. The signal extracted as a component corresponding to 
this photon density wave is compared with the signal of the predetermined 
frequency component of the originally incident modulated light to detect a 
quantitatively measurable predetermined parameter such as a phase 
difference (or a phase delay) .PHI. or an amplitude I.sub.p of the photon 
density wave at the detection point. 
This predetermined parameter has a predetermined relationship with an 
equivalent scattering coefficient .mu..sub.s ' of the scattering 
constituent and an absorption coefficient .mu..sub.a of the absorptive 
constituent of the scattering medium. For this reason, when a plurality of 
predetermined parameters obtained for waves having two or more different 
predetermined frequency components are arithmetically processed on the 
basis of a finding (e.g., a relation from which the influence of 
scattering is eliminated) disclosed by the present invention for the first 
time, various pieces of optical information (including the absorption 
coefficient, its linear integration value, and the concentration of a 
specific constituent) associated with absorption in the scattering medium 
can be obtained from the processed parameters. In addition, optical 
information (including an equivalent scattering coefficient of a scanning 
medium, its linear integration value, and the concentration of a specific 
constituent) associated with scattering can also be obtained, as needed. 
In this case, the equivalent scattering coefficient is defined as 
.mu..sub.s '=(1-g).mu..sub.s where g is the average cos.THETA. value with 
respect to a scattering angle .THETA., and .mu..sub.s is a scattering 
coefficient. The reciprocal number of .mu..sub.s ' is equal to the mean 
free path of light in the scattering medium. 
The predetermined parameter described above is exemplified as the phase 
difference .PHI.. Since the phase difference .PHI. serves as a function of 
the equivalent scattering coefficient .mu..sub.s ' and the absorption 
coefficient .mu..sub.s, a predetermined parameter .PHI..sub.1 for a photon 
density wave having a first predetermined frequency component having an 
angular frequency .omega..sub.1 and a parameter .PHI..sub.2 for a photon 
density wave having a second frequency component having an angular 
frequency .omega..sub.2 different from the angular frequency .omega..sub.1 
are obtained. Using the relationship (.PHI..sub.1, .omega..sub.1, 
.mu..sub.s ', .mu..sub.s) and the relationship (.PHI..sub.2, 
.omega..sub.2, .mu..sub.s ', .mu..sub.s), an absorption coefficient 
.mu..sub.a as the optical information of the scattering medium is 
obtained. In the simplest case, for example, when the ratio of .PHI..sub.1 
to .PHI..sub.2, i.e., .PHI..sub.1 /.PHI..sub.2 is obtained, the influence 
of the scattering constituent is eliminated to obtain a simple formula or 
relation. In any case, the signals corresponding to the parameters 
.PHI..sub.1 and .PHI..sub.2 are arithmetically processed on the basis of 
the above relationships to obtain the absorption coefficient .mu..sub.a 
serving as the optical information associated with absorption. Optical 
information such as the equivalent scattering coefficient .mu..sub.s ' and 
the concentration of a specific constituent is derived from signal 
processing using the .mu..sub.a value, as needed. 
In an optical information measuring apparatus for a scattering medium, 
optical information associated with scattering and absorption can be 
directly calculated without calculating a phase difference and the like as 
the predetermined parameters.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
1. Basic of Measurement of Optical Information in Scattering Medium 
Light (preferably, near-infrared rays in a living body or the like) which 
easily propagates through a living body is modulated with a sinusoidal 
wave between a kHz and GHz range. The behavior of modulated light in the 
medium upon incidence of the signal modulated with the sinusoidal wave or 
light constituting the modulated light can be derived from a photon 
diffusion theory. In this case, a sinusoidal photon density wave having a 
modulation angular frequency .omega. (frequency f=.omega./2.pi.) 
accompanies attenuation in the scattering medium, but coherently and 
regularly propagates in the scattering medium as a wave. This is 
theoretically and experimentally confirmed by Gratton et al..sup.5) and 
the present inventor. This wave will be called the photon density wave, 
hereinafter. The present inventor filed a patent application (Japanese 
Patent Application No. 4-192370) concerning an apparatus for measuring 
absorption information in a scattering medium and a method therefor. This 
apparatus and method use an approximated solution of a basic equation 
associated with the principle of the present invention. 
The behavior of each photon constituting the above modulated light or the 
photon density wave can be calculated by a computer. The behavior of the 
modulated light constituted by these photons can be analyzed, 
experimented, and examined in accordance with Monte Carlo calculation. The 
present inventor has made these analyses, experiments, and examinations in 
Monte Carlo calculation and experiments using standard samples to clarify 
the behavior of the modulated light or the photon density wave in the 
scattering medium, a method of quantitatively measuring a specific 
constituent in a scattering medium, and a method of imaging the modulated 
light and the specific constituent. 
The principle of basic operation of the present invention is clarified for 
the first time according to the above-mentioned analyses and experiments 
and will be described below. 
A photon diffusion equation is generally solved under the assumption that a 
point light source is located inside an infinitely spread scattering 
medium, as shown in FIG. 1. In this case, the photon density wave of the 
modulated frequency component (f=.omega./2.pi.) coherently propagates in 
the scattering medium, and the wave front of the photon density wave is 
concentrically spherical. 
To the contrary, in a practical apparatus, modulated light is incident on 
the outer surface of a scattering medium as in an imaging apparatus for 
measuring optical information (e.g., a scattering coefficient and an 
absorption coefficient) as one object of the present invention. In this 
case, the photon diffusion equation must satisfy the boundary condition on 
the surface of the scattering medium. This boundary condition is not to 
cause light or photon diffusion on the outer side of the scattering 
medium. FIG. 2 shows a state in which modulated light incident from a 
given point light source onto a slab-like scattering medium propagates in 
the scattering medium. In this case, at a location except for a location 
near the surface of the scattering medium, the photon density wave of the 
predetermined frequency component is regarded to coherently propagate like 
an almost spherical wave. Therefore, as in FIG. 2, the concentrically 
spherical photon density wave is regarded to propagate at a location 
except for the location near the surface of the scattering medium on the 
light source side. Such a spherical photon density wave is assumed in the 
following description. 
FIG. 3 shows a state in which spot-like modulated light is incident on the 
surface of the scattering medium, photons propagating through the 
scattering medium are detected by a photodetector practically having a 
certain input aperture, and a predetermined frequency component signal is 
extracted from an output signal from the photodetector. In this case, of 
all the photons detected by the photodetector, photons constituting the 
photon density wave of the predetermined frequency component are regarded 
to roughly propagate along the spindle-shaped principal optical path shown 
in FIG. 3. Reference symbol r in FIG. 3 denotes a distance from the light 
source to the photodetector (strictly speaking, the position at which 
light to be detected emerges from the scattering medium). The information 
detected utilizing the above wave involves the scattering and absorption 
coefficients of the spindle-shaped portion between the light incident 
point and the photodetection point. 
The above description has already been confirmed by Monte Carlo calculation 
and experiments using actual samples both by the present inventor. 
Modulated light of any waveform can be used to apply the above theory if 
it contains a predetermined frequency component of interest. For example, 
repeated pulsed light has wave components having the same frequency as the 
repetition frequency and frequencies which are integer multiples of the 
repetition frequency. The above theory is applied to any one of the above 
frequency wave components. The characteristics required for the modulated 
light are a stable repetition frequency and a stable light intensity. 
Even if modulated light is shaped into a broad beam, and the beam is 
incident on a scattering medium, the above theory can be applied. More 
specifically, if a wide beam of the modulated light is assumed to be 
incident on a scattering medium, this is equivalent to a case wherein a 
large number of point light sources are arranged on the upper surface 
(regarded as a plane) of a scattering medium. At a paraxial portion of a 
line connecting the modulated light incident point and the photodetection 
point, a plane photon density wave of the predetermined frequency 
component contained in the modulated light is regarded to propagate in the 
axial direction. 
The behavior of the modulated light in the scattering medium is precisely 
examined on the basis of the above concept, and a relationship between the 
predetermined parameters used in the present invention and the scattering 
coefficient of the scattering constituent and the absorption coefficient 
of the absorptive constituent in the scattering medium to be measured will 
be described in detail on the basis of an example. 
For descriptive convenience, incidence of light modulated with a sinusoidal 
wave in the form of a spot will be exemplified. The present invention is 
also applicable to repeated pulsed light and a repeated square photon 
density wave light and incidence of such light in the form of a parallel 
beam due to the same reason as described above. For the sake of 
descriptive simplicity, a solution derived from a photon diffusion 
equation is approximated in a simple form. However, a result to be 
obtained can be applied to a case using a more strict solution. 
2. Principle of Absorption Coefficient Measurement of Absorptive 
Constituent in Scattering Medium 
(1) Description of Propagation of photon density wave Having Predetermined 
Frequency Component by Photon Diffusion Theory 
When spot-like light which is modulated with a sinusoidal photon density 
wave of kHz to GHz is incident on the scattering medium, for example, the 
behavior of the spot-like light in the medium allows approximation of the 
following equation from the photon diffusion theory as follows. 
Assume that a point light source exists in a uniform scattering medium. A 
light intensity I(r,t) [photons/sec.multidot.mm.sup.2 ] at a position 
spaced apart from the point light source by a distance r at time t is 
represented as follows. Note that a modulated photon density wave which 
propagates through an infinitely spread scattering medium is assumed, but 
that the modulated photon density wave is also applicable to a scattering 
medium having a finite size. 
##EQU1## 
where S: the number of incident photons generated by a light source 
[photons/sec] 
M: the degree of modulation of the modulated light 
.omega.: the angular frequency [rad/sec] of the modulated wave 
.alpha.: the photon diffusion constant [mm.sup.2 /sec] 
.epsilon.: the fixed phase term 
D: the photon diffusion coefficient [mm] 
v: the speed [mm/sec] of light in the scattering medium (the speed of light 
in a vacuum is c=vn where n is the refractive index) 
g: the average value of cos.theta. with respect to the scattering angle 
.theta. 
.mu..sub.tr : the light attenuation coefficient [mm.sup.-1 ] 
.mu..sub.a : the absorption coefficient [mm.sup.-1 ] 
.mu..sub.s : the scattering coefficient [mm.sup.-1 ] 
.mu..sub.a ': the equivalent scattering coefficient [=(1-g).mu..sub.s ] 
At this time, a component I.sub.w (r,t) whose frequency is expressed as 
f=.omega./2.pi. is represented as follows. 
EQU I.sub.w (r,t)=(Sv/4.pi..alpha.r)M exp{-rA(.omega.)cos 
B(.omega.)-j[rA(.omega.)sin B(.omega.)-.omega.t+.epsilon.]}(1.5) 
Therefore, a phase difference .PHI. and an amplitude I.sub.p of the photon 
density wave represented by equation (1.5) are approximated as follows. 
EQU .PHI..apprxeq.rA(.omega.)sin B(.omega.) (1.6) 
EQU I.sub.p .apprxeq.(Sv/4.pi..alpha.r)M exp[-rA(.omega.)cos B(.omega.)] 
That is, 
EQU ln(SvM/4.pi..alpha.rI.sub.p).apprxeq.rA(.omega.)cos B(.omega.) (1.7) 
where in represents the natural logarithm. These approximations are used to 
make the following description. 
Equations (1.6) and (1.7) can be further simplified as follows. 
EQU If (.omega.v.mu..sub.a)=y&gt;0, 
then 
EQU A(.omega.)=(v.mu..sub.a /.alpha.).sup.1/2 (1+y.sup.2).sup.1/4 
##EQU2## 
That is, 
EQU .PHI..sup.2 =3[.mu..sub.a +(1-g).mu..sub.s ](r.sup.2 
/2v).times.{[.omega..sup.2 +(v.mu..sub.a).sup.2 ].sup.1/2 -v.mu..sub.a 
}(1.8) 
Similarly, from equation (1.7), 
EQU [ln(SvM/4.pi..alpha.rI.sub.p)].sup.2 =3[.mu..sub.a +(1-g).mu..sub.s 
](r.sup.2 /2v).times.{[.omega..sup.2 +(v.mu..sub.a).sup.2 ].sup.1/2 
+v.mu..sub.a } (1.9) 
Equations (1.8) and (1.9) represent approximated solutions of equation 
(1.1) for the photon density wave having the angular frequency .omega. 
coherently propagating in the scattering medium. These equations are used 
as the basic equations of the principle of the present invention. A more 
strict solution of the photon diffusion equation includes the second term, 
i.e., a correction term. However, the number of unknown quantities of this 
correction term is two, i.e., the equivalent scattering coefficient 
.mu..sub.s ' and the absorption coefficient .mu..sub.a, and it is not 
related to the form of the correction term. Therefore, as will be 
described later, the absorption coefficient .mu..sub.a and the equivalent 
scattering coefficient .mu..sub.s ' can be uniquely determined from two, 
simultaneous equations, representing measurement values .PHI..sub.1 and 
.PHI..sub.2 for the modulation angular frequencies .omega..sub.1 and 
.omega..sub.2. Note that the above relation and equations are disclosed 
for the first time by the present invention. 
A living body, a plant tissue, or the like can be one object to be measured 
of the present invention. In this case, generally, condition .mu..sub.a 
&lt;&lt;.mu..sub.s '=(1-g).mu..sub.s is satisfied. For example, parameter values 
for a standard living body are as follows. 
EQU .mu..sub.a =0.01 mm.sup.-1 
EQU .mu..sub.s =3 mm.sup.-1 
EQU g=0.85 
EQU .mu..sub.s '=(1-g).mu..sub.s =0.45 mm.sup.-1 
EQU n=1.33 
EQU v=3.times.10.sup.11 /1.33=2.26.times.10.sup.11 mm/sec 
EQU v.mu..sub.a =2.26.times.10.sup.9 =2.pi..times.3.6.times.10.sup.8 sec.sup.-1 
(1.10) 
Since .mu..sub.a &lt;&lt;.mu..sub.s '=(1-g).mu..sub.s, the following equation can 
be obtained from equations (1.8) and (1.9). 
EQU .PHI..sup.2 ={[3(1-g).mu..sub.s r.sup.2 ]/(2v)}.times.{[.omega..sup.2 
+(v.mu..sub.a).sup.2 ].sup.1/2 -v.mu..sub.a } (1.11) 
EQU [ln(SvM/4.pi..alpha.rI.sub.p)].sup.2 =[3(1-g).mu..sub.s r.sup.2 
/2v].times.{[.omega..sup.2 +(v.mu..sub.a).sup.2 ].sup.1/2 +v.mu..sub.a 
}(1.12) 
Equations (1.11) and (1.12) can be utilized for measuring a scattering 
medium satisfying condition .mu..sub.a &lt;&lt;.mu..sub.s '=(1-g).mu..sub.s. 
(2) Calculation of Absorption Coefficient 
To obtain the absorption coefficient, waves having two different frequency 
components (angular frequencies .omega..sub.1 and .omega..sub.2) are used. 
In this case, even if the angular frequencies are changed from 
.omega..sub.1 to .omega..sub.2 in the same scattering medium while other 
parameters are kept constant, the scattering and absorption coefficients 
of the scattering medium remain the same because the light wavelength is 
constant. When modulated light components having two angular frequencies 
.omega..sub.1 and .omega..sub.2 are incident on a scattering medium at a 
given position and are detected at another given position, r remains the 
same. It should be noted that a large error occurs due to the difference 
of scattering coefficients for these two wavelengths. 
If the measurement values .PHI. of the predetermined parameter 
corresponding to the detected waves are as follows: 
EQU .PHI.=.PHI..sub.1 for .omega.=.omega..sub.1 
EQU .PHI.=.PHI..sub.2 for .omega.=.omega..sub.2 (1.13) 
the following equation is derived from equation (1.8). 
EQU .PHI..sub.1.sup.2 /.PHI..sub.2.sup.2 ={[.omega..sub.1.sup.2 
+(v.mu..sub.a).sup.2 ].sup.1/2 -(v.mu..sub.a)}.div.{[.omega..sub.2.sup.2 
+(v.mu..sub.a).sup.2 ].sup.1/2 -(v.mu..sub.a)} (1.14) 
In this case, v is known or can be measured or calculated by other methods. 
For example, water is a major component of the living body. The value v is 
given by equation (1.10) described above. Substitutions of the known value 
v, the values of the predetermined .omega..sub.1 and .omega..sub.2, and 
the values of .PHI..sub.1 and .PHI..sub.2 as measurement values into 
equation (1.14) uniquely yield the absorption coefficient .mu..sub.a of 
the absorptive constituent of the scattering medium. The calculation of 
obtaining this .mu..sub.a can be executed using a computer at high speed. 
Substitutions of the value .mu..sub.a and the value r determined by the 
measuring system into equation (1.8) yield the equivalent scattering 
coefficient .mu..sub.s '=(1-g).mu..sub.s. 
Since the values .PHI..sub.1 and .PHI..sub.2 are measurement values, their 
precision is limited to, e.g., about 0.1.degree. (1.75.times.10.sup.-3 
rad). As is apparent from equation (1.14), to obtain .mu..sub.a with high 
accuracy, .omega..sub.1 and .omega..sub.2 are preferably selected to have 
almost the same order as that of the v.mu..sub.a value (for example, 
.omega..sub.1 and .omega..sub.2 are about 10.sup.8 to 10.sup.10 because 
v.mu..sub.a =2.26.times.10.sup.9 for v=2.26.times.10.sup.11 mm/sec and 
.mu..sub.a =0.01.times.10.sup.-3 mm.sup.-) or .omega..sub.1 and 
.omega..sub.2 are preferably selected to satisfy condition .omega..sub.1 
&lt;v.mu..sub.a &lt;.omega..sub.2 or conversely .omega..sub.1 &gt;v.mu..sub.a 
&gt;.omega..sub.2. In addition, when the number of predetermined frequencies 
is three or more, an improvement of measurement precision can be expected. 
A method of using the ratio .PHI..sub.1.sup.2 /.PHI..sub.2.sup.2 is 
exemplified as a practical method of obtaining the absorption coefficient 
.mu..sub.a based on the relationship between .PHI..sub.1 and .omega..sub.1 
and the relationship between .PHI..sub.2 and .omega..sub.2. Any form may 
be used if these relationships are derived from equation (1.8) or an 
equation representing a more strict solution of the photon diffusion 
equation, as described above. Since these relationships can be expressed 
by simultaneous equations including two unknown quantities, the absorption 
coefficient .mu..sub.a and the equivalent scattering coefficient 
.mu..sub.s ', the two unknown quantities can be uniquely determined. When 
a simple approximated solution is used for example, .PHI..sub.1 
/(.PHI..sub.2, (.PHI..sub.1.sup.2 -.PHI..sub.2.sup.2)/(.PHI..sub.1.sup.2 
-.PHI..sub.3.sup.2), or the like may be used. In this case, .PHI..sub.3 is 
a phase difference obtained in response to an angular frequency 
.omega..sub.3. 
To measure parameters for three different predetermined frequencies, a 
method of obtaining (.PHI..sub.1 -.PHI..sub.2)/(.PHI..sub.1 -.PHI..sub.3) 
and then calculating the absorption coefficient .mu..sub.a can be used, 
although the equation form is slightly complicated. In this case, since 
(.PHI..sub.1 -.PHI..sub.2) and (.PHI..sub.1 -.PHI..sub.3) are differences 
between the phase differences, the origin (zero point) of the phase 
difference .PHI. need not be detected and then it facilitates actual 
measurements. 
A similar result can be obtained for the amplitude I.sub.p by considering 
the logarithm expressed in equation (1.9). In this case, a photon 
diffusion constant .alpha. or a photon diffusion coefficient D must be 
separately obtained. For example, as can be apparent from equation (1.4), 
the photon diffusion coefficient D can be obtained by actually measuring 
an absorption coefficient in absorbance measurement. 
As described above, the phase difference .PHI. and the amplitude I.sub.p as 
the predetermined parameters can be equally processed although the forms 
of equations are different from each other. For the sake of descriptive 
simplicity, the phase difference .PHI. as the predetermined parameter will 
be exemplified. The phase difference .PHI. requires a simpler equation 
than the amplitude I.sub.p. 
It should be noted that the influence of the scattering constituent is 
eliminated from equation (1.14). That is, equation (1.14) indicates that 
the absorption coefficient of an absorptive constituent in a scattering 
medium containing a scattering constituent can be measured with high 
precision. This naturally results from the basic principle of the present 
invention based on measurement using two different angular frequencies 
.omega..sub.1 and .omega..sub.2 in equation (1.8). Therefore, this 
indicates that the equivalent scattering coefficient .mu..sub.s ' and the 
absorption coefficient .mu..sub.a can be uniquely obtained by the present 
invenion. Various expression forms such as the above-mentioned method of 
obtaining a more strict solution are available to obtain the absorption 
coefficient .mu..sub.a. 
Judging from the above description, the equivalent scattering coefficient 
and the absorption coefficient of an intralipid solution serving as a 
standard scattering medium sample whose high-precision measurement is 
conventionally difficult can be measured. The present invention thus has a 
very high usefulness. That is, the absorption coefficient and the 
equivalent scattering coefficient can be accurately measured by the 
present invention if a scattering medium has scattering and absorption 
properties. 
This new finding of the present invention is utilized in quantitative 
measurement of the concentration of an absorptive constituent as another 
object of the present invention. The concentration of a specific 
constituent is obtained from the absorption coefficient in accordance with 
the Lambert-Beer law. 
The absorption coefficient .mu..sub.a thus obtained is an axial integration 
value of the absorption coefficient .mu..sub.a of a spindle-shaped portion 
having the length r along a straight line obtained by connecting a point 
at which modulated light is incident on the scattering medium and a 
photodetection point. If this value is regarded as a linear integration 
value along this straight line, a tomogram associated with the absorption 
coefficient .mu..sub.a can be obtained using simple imaging and image 
reconstruction as in X-ray CT. In addition, by similar processing, imaging 
and reconstruction of a tomogram can be performed for hemoglobin 
saturation and an absorptive constituent distribution. Imaging and 
reconstruction of a tomogram can also be performed for the scattering 
coefficient. 
3. Measurement of Absorption Information 
As described above, the absorption coefficient is obtained by equation 
(1.14) and the like. Assume measurements using light components having 
different wavelengths or measurements at different times and places. The 
principle of measurement for typical examples will be described below. The 
detailed arrangements of these measurement apparatuses will be described 
in detail in the description of preferred embodiments. 
(1) Measurement of Concentration of Hemoglobin 
Main absorptive constituents in a mammalian brain are water, cytochrome, 
oxyhemoglobin, and reduced hemoglobin. Absorption of water and cytochrome 
in a near-infrared range is negligibly small with respect to oxyhemoglobin 
and reduced hemoglobin. Oxyhemoglobin and reduced hemoglobin have 
different absorption spectra, as shown in FIG. 4. The skull is regarded as 
a scattering medium with respect to near-infrared rays. 
If setup is fixed by the method described in the above section, and the 
absorption coefficients .mu..sub.a1 and .mu..sub.a2 are obtained for two 
modulated light components having wavelengths .lambda..sub.1 and 
.lambda..sub.2, respectively, the following equations are established in 
accordance with the Lambert-Beer law as follows. 
.mu..sub.a1 =.epsilon..sub.Hb,1 [Hb]+.epsilon..sub.Hb0,1 [HbO] 
.mu..sub.a2 =.epsilon..sub.Hb,2 [Hb]+.epsilon..sub.Hb0,2 [HbO] 
where 
.epsilon..sub.Hb,1 : the molar absorption coefficient [mm.sup.-1 
.multidot.M.sup.-1 ] of reduced hemoglobin at the wavelength 
.lambda..sub.1 
.epsilon..sub.Hb0,1 : the molar absorption coefficient [mm.sup.-1 
.multidot.M.sup.-1 ] of oxyhemoglobin at the wavelength .lambda..sub.1 
.epsilon..sub.Hb,2 : the molar absorption coefficient [mm.sup.-1 
.multidot.M.sup.-1 ] of reduced hemoglobin at the wavelength 
.lambda..sub.2 
.epsilon..sub.Hb0,2 : the molar absorption coefficient [mm.sup.-1 
.multidot.M.sup.-1 ] of oxyhemoglobin at the wavelength .lambda..sub.2 
[Hb]: the molar concentration [M] of reduced hemoglobin 
[HbO]: the molar concentration [M] of oxyhemoglobin 
The molar concentration [Hb] of reduced hemoglobin and the molar 
concentration [HbO] of oxyhemoglobin can be obtained from the coefficients 
.mu..sub.a1 and .mu..sub.a2 calculated from the measured values, and the 
known parameters .epsilon..sub.Hb,1, .epsilon..sub.Hb0,1, 
.epsilon..sub.Hb,2, and .epsilon..sub.Hb0,2. 
When quantitative measurement of the concentrations of three constituents 
whose absorption spectra are known in such a case that the cytochrome or 
the like is taken into consideration, three-wavelength light is used. In 
quantitative measurement of the concentrations of n constituents whose 
absorption spectra are known, the measurement values of the absorption 
coefficients at n wavelengths are generally used to obtain the values in 
the same manner as described above. 
Since the degree Y of saturation is given as follows: 
EQU Y=[HbO]/([Hb]+[HbO]) 
the following equation is obtained. 
EQU .mu..sub.a1 /.mu..sub.a2 =[.epsilon..sub.Hb,1 +Y(.epsilon..sub.Hb0,1 
-.epsilon..sub.Hb,1)]+[.epsilon..sub.Hb,2 +Y(.epsilon..sub.Hb0,2 
-.epsilon..sub.Hb,2)] 
Y is calculated from the known parameters .epsilon..sub.Hb,1, 
.epsilon..sub.Hb0,1, .epsilon..sub.Hb,2, and .epsilon..sub.Hb0,2 and the 
coefficients .mu..sub.a1 and .mu..sub.a2 calculated from the measured 
values. 
In the above method, absorption coefficients respectively corresponding to 
the wavelengths of light components are accurately obtained by the method 
disclosed for the first time by the present invention. The wavelength 
dependency of the equivalent scattering coefficient which poses a problem 
in the conventional absorbance measuring method need not be considered, 
and measurement errors caused by this method can be eliminated. If a 
wavelength (.apprxeq.800 nm, isosbestic wavelength) for obtaining the same 
absorption level for both oxyhemoglobin and reduced hemoglobin is used, 
the above equation can be made simpler. 
(2) Measurement of Change in the Concentration of Absorptive Constituents 
over Time 
When the measurements described above are performed at different times, a 
change in the concentration of absorptive constituents over time or a 
change in absorption coefficient over time, a change in concentration of 
the absorptive constituent over time, a change in saturation over time, a 
change in equivalent scattering coefficient over time, a change in 
concentration of the scattering constituent over time, and the like can be 
measured. 
(3) Imaging 
The measurement values of the scattering information and the absorption 
information which are obtained by the above method are regarded as linear 
integration values of optical information such as the equivalent 
scattering coefficient, the absorption coefficient, the concentration of 
the specific constituent, and the degree of saturation in the scattering 
medium, which are included in the spindle-shaped portion along the 
straight line obtained by connecting the spot-like modulated light 
incident position to the photodetection point. When the above measurements 
are performed at a large number of locations on a relatively thin (i.e., 
the distance r is small) scattering medium, a two-dimensional distribution 
measurement, i.e., imaging can be performed. In this case, it is more 
convenient to use a value normalized with the distance r. The distance r 
can be easily measured by a conventional distance measuring apparatus. A 
plurality of photodetectors can also be utilized. 
(4) Measurement of Tomogram 
Multi-point measurement is performed along a slice of the scattering medium 
to obtain the above linear integration value of absorption coefficient or 
the concentration of the specific constituent as in (1). The resultant 
absorption coefficient or the concentration of the specific constituent is 
used to obtain a tomogram as in X-ray CT. In this case, the value 
normalized with the distance r is used. A plurality of photodetectors can 
also be used. 
(5) Arrangement of Measuring Apparatus 
FIG. 5 shows a detailed arrangement of a scattering medium optical 
information measuring apparatus according to the present invention. A 
light source 2 is driven in accordance with an output signal from a 
repetition signal generator 1 and generates modulated light having two 
predetermined angular frequency components .omega..sub.1 and 
.omega..sub.2. In this case, this light source can generate a plurality of 
modulated light components for each of light components having a plurality 
of different wavelengths. In this case, a method of synthesizing light 
components having a plurality of different wavelengths from a light source 
or a method of switching between the light components along the time axis 
can be used. 
A desired wavelength of the modulated light can be selected by a wavelength 
selecting means 3 such as a spectral band pass filter. The modulated light 
having the selected wavelength is focused and incident on one point on the 
surface of a scattering medium 22 serving as an object to be measured. 
Light propagating in the scattering medium is detected by a photodetector 
8 having an aperture at a position (photodetection point) opposite to the 
modulated light incident point of the scattering medium. A first unit 10 
extracts sinusoidal waves respectively corresponding to the two 
predetermined angular frequency components .omega..sub.1 and .omega..sub.2 
from the signal from the photodetector. These extracted sinusoidal waves 
are compared with a reference signal (preferably a sinusoidal wave) 
synchronized with the modulated light. A parameter, e.g., a phase 
difference, associated with each photon density wave changed during 
propagation through the scattering medium is obtained. The wavelength of 
the modulated light incident on the scattering medium is changed to obtain 
a predetermined parameter in the same manner as described above. 
An arithmetic processing means 17 serving as a second unit calculates 
optical information associated with scattering and absorption on the basis 
of a plurality of predetermined parameters. More specifically, using the 
relationship between the phase difference as a predetermined parameter, 
represented in equation (1.14), and the equivalent scattering and 
absorption coefficients of the scattering medium, the absorption 
coefficient and the equivalent scattering coefficient are obtained by 
operation. A plurality of absorption coefficients are obtained from a 
plurality of predetermined parameters, i.e., a plurality of phase 
differences for modulated light components having different wavelengths. 
Using the resultant values, the concentration of a specific constituent, 
the degree of hemoglobin saturation, and the like are calculated. 
The position of the incident point of the modulated light incident on the 
scattering medium and the position of the photodetection point are scanned 
(not shown) to obtain information associated with absorption at each 
portion of the scattering medium, e.g., the degree of hemoglobin 
saturation. When the obtained information is stored in a frame memory (not 
shown) and is read out in accordance with a television scheme, an image 
representing a distribution of the saturation degree is obtained. A 
display recording means 18 is used in such data display recording. In this 
case, the distance r between the modulated light incident point and the 
photodetection point is measured, and the value normalized with the 
distance r is used. A tomogram can be reconstructed using this value as in 
X-ray CT. 
The arrangements of the respective components of the scattering medium 
optical information measuring apparatus will be described below. These 
components are also used in various embodiments to be described below. 
Modulated light containing at least two predetermined frequency components 
is generated using current modulation of a laser diode, as shown in FIG. 
6. In this case, a current used to drive the laser diode is generated by 
causing an adder to add the two sinusoidal waves having the predetermined 
frequency components. 
Also, as previously described, this light source may generate pulsed light 
or a square wave. The laser diode can easily generate these modulated 
light components by current modulation. In addition to this, a method of 
generating modulated light using beating of a CW laser or an optical 
modulator is also available. The two different frequency components may be 
switched along the time axis and may be generated in a time division 
manner. 
The modulated light components having different wavelengths can be 
generated using a plurality of light sources having different wavelengths. 
These light components may be simultaneously output or may be switched and 
output in a coaxial manner using a half mirror. An optical switch may be 
utilized in wavelength selection. In addition, the coaxial modulated light 
components having different wavelengths may be selected by a wavelength 
selection filter at a position immediately before the light incident 
position or at a position immediately before a photodetector upon direct 
incidence of these parallel modulated light components on the scattering 
medium. 
To cause the above-mentioned modulated light to be incident on a scattering 
medium such as a living body, a method utilizing a condenser lens (FIG. 
7A), an optical fiber (FIG. 7B), or a pinhole (FIG. 7C), or a modulated 
light incident method using a gastrocamera (FIG. 7D) or the like may be 
used. 
A means for detecting the changed modulated light propagating through the 
scattering medium may be constituted by direct photodetection (FIG. 8A), a 
method of detecting the light through an optical fiber and a lens (FIGS. 
8B and 8C), a heterodyne detection method of a specific frequency 
component (FIG. 8D), or the like. 
The means for extracting the signal having the specific frequency signal 
may be constituted by a method using a narrow-band amplifier (FIG. 9A), a 
method using a lock-in amplifier (FIG. 9B), a heterodyne type lock-in 
amplifier (FIG. 9C), or the like. A reference signal synchronized with the 
modulated light is required in the method using the lock-in amplifier. The 
output signal from the repetition signal generator 1 shown in FIG. 5 is 
used as this reference signal. When the modulated light contains two 
predetermined frequency components, an input to the lock-in amplifier is 
not changed, and only the reference signal is switched, thereby extracting 
signals having two different predetermined frequency components. 
A scanning means for imaging may be constituted by a method of scanning the 
pair of light source and photodetector (FIG. 10A), a method of moving the 
scattering medium as the object to be measured (FIG. 10B), or the like. To 
measure a tomogram, rotary scanning of the scattering medium or the pair 
of light source and photodetector is required as in X-ray CT. Rotary 
scanning may be performed simultaneously with translational scanning. In 
addition, as shown in FIG. 11, a method of causing a plurality of 
photodetectors D.sub.1, D.sub.2, . . . to detect a photon density wave 
concentrically spherically propagating through the scattering medium is 
also available. This method is used in imaging and measurement of a 
tomogram. Note that optical information obtained by each photodetector 
must be normalized in accordance with a distance r between each 
photodetector and the modulated light incident position. 
Generation of the modulated light, selection of a wavelength, modulated 
light incidence, photodetection, signal extraction, predetermined 
parameter detection, scanning, and the like described above can be applied 
when a light source generates various type of repetition pulses. 
Arithmetic processing of the degree of saturation of hemoglobin, the 
concentration of a specific constituent, and other absorption information 
in a scattering medium, and tomograms thereof is performed at high speed 
using a computer having a memory, a display, and the like. 
4. Detailed Embodiments 
(1) First Embodiment (Measurement of Absorption Coefficient and the like of 
Scattering Medium) 
FIG. 12 shows the first embodiment of the scattering medium optical 
information measuring apparatus according to the present invention. 
A light source 2 utilizing a laser diode generates modulated light 
I=I.sub.0 (2+M.sub.1 cos.omega..sub.1 t+M.sub.2 cos.omega..sub.2 t) (where 
I.sub.0 is a constant, M.sub.1 and M.sub.2 are the degrees of modulation 
at angular frequencies .omega..sub.1 and .omega..sub.2, and t is time) 
having a predetermined wavelength in accordance with a signal from a 
repetition signal generator 1. 
The wavelength of light from the light source must be appropriately 
selected in accordance with the type of object to be measured. Light 
having a wavelength of 700 nm or more generally easily propagate in a 
living body in relation to absorption of hemoglobin and the like. As shown 
in FIG. 4, oxyhemoglobin and reduced hemoglobin have different spectral 
transmittances. If a plurality of wavelengths are used, oxyhemoglobin and 
reduced hemoglobin can be separately measured. 
The resolving power such as imaging in the scattering medium can be 
increased at higher angular frequencies .omega..sub.1 and .omega..sub.2 
contained in the modulated light, but signal attenuation is undesirably 
increased. In general, measurement accuracy can be improved when the 
difference between the angular frequencies .omega..sub.1 and .omega..sub.2 
is increased. It is also preferable to select a frequency which can 
facilitate the arrangement of a modulated light source, signal extraction 
in the subsequent stage, predetermined parameter detection, and the like. 
Three or more different frequencies can be used to further improve the 
measurement accuracy. 
Various types of light sources such as an He-Ne laser can be used in 
addition to the laser diode. A light source which can facilitate the 
circuit arrangement for generating modulated light is preferably selected. 
A light source may generate pulsed light or square photon density wave 
light. A larger degree of modulation is preferred, but a smaller degree of 
modulation does not pose any essential problem. The degree of modulation 
may be determined in favor of the arrangement of the modulation apparatus. 
When a laser diode is used as a light source, a drive current can be 
modulated to easily produce modulated light of about several kHz to 1 GHz. 
When the frequency exceeds 1 GHz, a laser diode having good frequency 
characteristics and a high-frequency circuit are required. The modulated 
light containing the plurality of frequency components can be easily 
generated by a circuit shown in FIG. 6. The light beams may be generated 
by different laser diodes and may be synthesized, or the different light 
beams may be switched along the time axis. 
The modulated light from the light source is incident on an object 
(scattering medium) 22 to be measured serving as a scattering medium 
through an optical fiber 4. In this case, as described in the previous 
paragraph, the modulated light may be collimated, and the collimated light 
may be focused using a condenser lens or pinhole. More specifically, since 
a diffusion length l.sub.d =1/(1-g).mu..sub.s is about 3 mm or less in a 
scattering medium, the incident light is almost perfectly scattered before 
it propagates straight by about 3 mm, and directivity of incident light is 
lost. When a scattering medium having a thickness of several mm or more is 
taken into consideration, a condition for causing the modulated light to 
be incident as a light spot must be satisfied. As described before, the 
modulated light may be shaped into a broad beam, the broad beam may be 
caused to become Incident on the scattering medium and the photodetector 
may be arranged on the side of the scattering medium opposite to the 
modulated light incident position along the optical path of this light 
beam. 
A space between the optical fiber 4 and the object (scattering medium) 22 
is very small in the embodiment of FIG. 12. However, in practice, this 
space may be filled with a liquid material or jelly-like material (to be 
referred to an interface material hereinafter) having almost the same 
refractive index and scattering coefficient as those of the object 22. 
That is, the photon density wave having the predetermined frequency 
component coherently propagates in this interface material and becomes 
incident on the object, thus posing no problem. 
A photodetector 8 has an aperture 6 for controlling an effective area of 
light-receiving surface. The aperture 6 may be a hole formed on opaque 
plate. When light is guided to the photodetector through an optical fiber 
or a light guide, the end face of the optical fiber or the like serves as 
an effective aperture. In either case, it is preferable to have a 
structure in which light incident on a portion except the active area of 
the photodetector is shielded. In addition, the interface medium may be 
inserted between the photodetection aperture 6 and the object 22. If the 
modulated light propagating in the scattering medium contains light 
components having a plurality of wavelengths, a wavelength selection 
filter (not shown) is inserted between the aperture 6 and the 
photodetector 8. 
Any photodetector such as a phototube, a photodiode, an avalanche 
photodiode, or a PIN diode can be used as the photodetector 8 in addition 
to a photomultiplier. Any photodetector can be selected if it has spectral 
sensitivity characteristics and frequency characteristics enough to detect 
the modulated light having the predetermined frequency component of the 
light having the predetermined wavelength. If output light is weak, a 
high-sensitivity photodetector is used. 
An output signal from the photodetector is input to a lock-in amplifier 10. 
The lock-in amplifier 10 accurately extracts waves having predetermined 
frequency components (in this case, the waves having the angular 
frequencies .omega..sub.1 and .omega..sub.2) from a photodetection signal. 
The extracted waves are compared with the reference signal from the 
repetition signal generator 1 to detect a phase difference and an 
amplitude which serve as predetermined parameters corresponding to these 
waves. In FIG. 12, a function of extracting the signal having the 
predetermined frequency component is represented as signal extraction 11, 
and a function of detecting the predetermined parameters is represented as 
parameter detection 12. 
FIG. 13 shows an arrangement of the main part of this lock-in amplifier. 
The lock-in amplifier can precisely select and detect only a component 
having the same frequency as and a predetermined phase relationship with a 
reference signal from a small repeated signal mixed in noise. The weak 
input signal is amplified with a narrow band, and the amplified signal is 
multiplied with the reference signal or synchronously rectified (also 
called phase sensitive detection), and an integration value thereof is 
output. Any reference signal can be used if it is synchronized with the 
input signal to be measured. In this embodiment, the output signal from 
the repetition signal generator 1 is used, but a signal obtained upon 
reception of the modulated light on another photodetector may be used as 
the reference signal. 
The waveforms of the respective signals in this lock-in amplifier are shown 
in FIG. 14. FIG. 14(a) shows an input signal, FIG. 14(b) shows an output 
from the narrow-band amplifier, FIG. 14(c) shows an output from a phase 
circuit, FIG. 14(d) shows an output from the multiplier or a synchronously 
detected output, and FIG. 14(e) shows an output from the integrator. The 
signal-to-noise ratio (S/N ratio) of the detection system using the 
lock-in amplifier is determined by an equivalent noise bandwidth .DELTA.f 
of the system and is in inverse proportion to (.DELTA.f).sup.1/2. 
In this lock-in amplifier, as shown in FIG. 15, an output corresponding to 
a signal sin(.omega.t-.PHI.) (FIG. 15(a)), which is phase-delayed by .PHI. 
from the reference signal (FIG. 15(b)) is Acos.PHI.. An average value of 
the synchronously detected output becomes maximum when .PHI.=0. Note that 
A is a constant. Therefore, by sifting the phase of the reference signal 
from the phase circuit shown in FIG. 13, the phase of the input signal 
(FIG. 14(a)) to the lock-in amplifier can be known from a shift amount of 
the phase of the reference signal which maximizes the synchronously 
rectified output, i.e., when .PHI.=0. 
A commercially available lock-in amplifier responds up to several MHz. In a 
lock-in amplifier of several MHz to 1 GHz, the operational principle is 
the same as that of the above commercially available lock-in amplifier, 
but must be arranged using a high-speed electronic device. In the region 
of several MHz to 1 GHz, a heterodyne amplifier is generally connected to 
the input to the narrow-band amplifier in FIG. 13. This lock-in amplifier 
is called a heterodyne type lock-in amplifier. The arrangement of this 
heterodyne type lock-in amplifier is illustrated in FIG. 9C. The 
heterodyne amplifier has a function of converting the input signal into a 
signal representing a difference between the frequency of the input signal 
and the oscillation frequency of a local oscillator. This difference 
signal, i.e., a signal having an intermediate frequency of several MHz or 
less is input to the lock-in amplifier described above. In this case, the 
reference signal is a signal synchronized with the intermediate frequency. 
A conventional commercially available lock-in amplifier outputs an 
amplitude I.sub.p of the signal of the predetermined frequency extracted 
from the photodetection signal from the photodetector 8, an amplitude 
obtained upon separation into two orthogonal components, or a phase 
difference .PHI. between the input signal and the reference signal. A 
function of generating this output is included in parameter detection 12 
in the lock-in amplifier 10 in FIG. 12. 
In this embodiment, of all the parameters described above, the phase 
difference between the input signal and the reference signal is used. When 
a phase difference .PHI. in which an offset component such as a phase 
delay generated in a modulated light incident optical fiber or the like is 
corrected is used, this phase difference .PHI. corresponds to the phase 
delay of the photon density wave having the predetermined frequency 
component and propagating in the scattering medium as the object to be 
measured, i.e., the phase difference .PHI. in equation (1.8). This offset 
component is determined by the arrangement of the apparatus and serves as 
a constant. The offset component may be actually measured. In this manner, 
the phase differences .PHI..sub.1 and .PHI..sub.2 corresponding to the two 
predetermined frequencies .omega..sub.1 and .omega..sub.2 are obtained and 
correspond to the phase differences .PHI..sub.1 and .PHI..sub.2 calculated 
in equation (1.14), respectively. 
An arithmetic processing means 17 in FIG. 12 calculates the absorption 
coefficient .mu..sub.a of the scattering medium as the object to be 
measured, using the resultant .PHI..sub.1 and .PHI..sub.2. More 
specifically, the absorption coefficient .mu..sub.a is obtained using 
equation (1.14) or the like. This operation can be easily performed at 
high speed by a microcomputer incorporated in the arithmetic processing 
means. Optical information such as the equivalent scattering coefficient 
.mu..sub.s ' of the scattering medium as the object can be calculated 
using the resultant .mu..sub.a value, and optical information such as the 
concentration of the absorptive constituent can also be calculated using 
the spectral absorbance of the specific absorptive constituent, as needed. 
If a scattering medium contains a plurality of absorptive constituents, 
modulated light having a plurality of wavelengths is used, as previously 
described. In this case, a method using modulated light containing light 
components having a plurality of different wavelengths or a method of 
measuring optical information for the plurality of different wavelengths 
in a time division manner may be used, as described earlier. A distance r 
between the incident position of the modulated light incident on the 
scattering medium as the object and the photodetection position is 
measured using a distance measuring unit 20 in FIG. 12, and the 
measurement is normalized using the value r, thereby obtaining an 
absorption coefficient per unit distance, a concentration per unit 
distance, and the like. 
When measurement of various pieces of optical information is performed at a 
different time, e.g., t.sub.1 after the above measurement while the 
arrangement remains the same, changes in these pieces of optical 
information over time can be measured. The arithmetic processing means 17 
has a function of storing optical information values thus obtained, and a 
display recording means 18 in FIG. 12 displays or records the information. 
In the embodiment shown in FIG. 12, a pair of modulated light incident 
position and photodetection position can be scanned or moved (not shown) 
with respect to the scattering medium 22 as the object to be measured. In 
this case, measurements of the various pieces of optical information are 
performed at different times and different locations. If the distance r 
remains the same in the measurements at different locations, and the 
scattering medium (object) 22 is set in a steady state, the spatial 
distribution of the optical information can be measured. When the distance 
r varies depending on different locations, optical information normalized 
by the distance r values as outputs from the distance measuring unit 20 is 
used. 
(2) Second Embodiment (Tomographic Measuring Apparatus) 
FIG. 16 is a view showing an arrangement of an apparatus of the second 
embodiment to explain tomographic measurement of a scattering medium. In 
the first embodiment, light constituting a photon density wave having a 
predetermined frequency component is detected in a predetermined direction 
of optical axis, and various types of optical information contained in a 
spindle-shaped portion in the scattering medium along the optical axis are 
measured. However, in the second embodiment, an object 22a to be measured 
or a pair of modulated light incident position and photodetection position 
are rotated and scanned with respect to a scattering medium as an object 
22a to be measured so that the direction of optical axis becomes each of 
all directions. Using various types of optical information obtained as in 
the first embodiment, a tomogram is reconstructed as in X-ray CT (Computer 
Tomography). 
The basic arrangement shown in FIG. 16 is substantially the same as that of 
FIG. 12, except for a portion for holding the object 22a, a wavelength 
selecting means 3, a light guide 9, a tomographic reconstruction signal 
processing means 19, and the like. 
A light source 2 generates modulated light I=I.sub.0 (2+M.sub.1 
cos.omega..sub.1 t+M.sub.2 cos.omega..sub.2 t) of light having a 
predetermined wavelength in accordance with a signal from a repetition 
signal generator 1. The desired wavelength of the modulated light from the 
light source is selected by the wavelength selecting means 3, and the 
modulated light having the selected wavelength is incident, through an 
optical fiber 4, on an object 22a to be measured surrounded by an 
interface material 23. The interface material 23 has the optical 
characteristics described above and is surrounded by a thin-film vessel 
having a low reflectance. Light incident on the vessel containing the 
interface material is hardly reflected on the interface between the vessel 
and the interface material. If the outer and inner surfaces of the thin 
film are rough surfaces, the incident light has light components which 
propagate in all directions. With this arrangement, the modulated photon 
density wave propagates through the interface material and the object 22a 
and reaches a photodetection point located on the opposite side. The light 
guide 9 is located at the photodetection point, and it is coupled to the 
photodetector 8, so that the light is incident on the photodetector 8 
through this light guide. The interior of the vessel containing the 
interface material except for a portion around an opening of the light 
guide and a portion around a light incident aperture is preferably 
constituted by an absorption medium with respect to light. Therefore, 
light reflection on the inner surface can be eliminated, and accurate 
measurements can be performed. 
The object 22a is rotated relative to the light source optical fiber 4, the 
photodetection light guide 9, the interface material 23, and the vessel. 
The vessel must have a structure that although the interface vessel has a 
circular outer cross-section, the interior of the vessel conforms to the 
shape of object 22a to be measured, and no gap is formed even if the 
object 22a is rotated. This structure can be achieved by a method of 
preparing one vessel which surrounds the object 22a, as shown in FIG. 16, 
or a method of preparing two vessels respectively on the light incident 
and exit sides as shown in FIG. 17. In either case, the interface material 
must be brought into tight contact with the light incident and 
photodetection apertures, and at the same time, the inner side of the 
interface material can be brought into contact with the object 22a to be 
measured by utilizing the gravity or a pressure. 
An optical signal obtained as described above is processed in the same 
manner as in the first embodiment to obtain optical information 
corresponding to optical axes of all directions of the object 22a. 
Therefore, image reconstruction as in X-ray CT can be performed by a 
signal processing means 19, and a tomogram can be obtained by an image 
display recording means 18. Even if the object 22a to be measured is 
rotated, and other members are kept stationary in the arrangement of FIG. 
16, the same measurement as described above can be performed. 
The tomograms obtained in this embodiment represent an absorption 
coefficient distribution, a scattering coefficient distribution, a 
concentration distribution of a specific constituent, and a distribution 
of the degree of saturation of oxyhemoglobin all in a scattering medium. 
(3) Third Embodiment (Utilization of a Plurality of Photodetectors) 
A plurality of photodetectors are used in the third embodiment. Equations 
(1.1) to (1.4) are established in all directions within a scattering 
medium. For this reason, a plurality of photodetectors can be used, as 
shown in FIG. 11. With this arrangement, the distribution of optical 
information of the scattering medium like a panoramic image is obtained by 
viewing an object from the light incident point in a wide range. In this 
case, the plurality of photodetectors can be arranged on the outer surface 
of the scattering medium at arbitrary positions. This arrangement makes it 
possible to shorten the measurement time as compared with a scheme in 
which one photodetector is moved from D.sub.1 to D.sub.5. When the pitch 
between the adjacent photodetectors is large, the photodetector array may 
be rotated and scanned about the light incident point to obtain an image 
having a higher sampling density. In this case, the interface material as 
shown in the second embodiment may be used, and measurements of objects 
having different distances depending on the directions can be performed. 
End faces of a plurality of optical fibers having the same length may be 
located at the positions of the photodetectors, and opposite ends of the 
optical fibers may be connected to the plurality of photodetectors or the 
photodetector array. If the distances r are different from each other, the 
distance r is preferably measured by another method, and the various types 
of optical information are preferably normalized with the resultant values 
r. The interface medium shown in the second embodiment may be utilized. 
(4) Fourth Embodiment (CT Using a Plurality of Photodetectors) 
The fourth embodiment is obtained by adding the arrangement of the third 
embodiment to the tomographic measuring apparatus of the second 
embodiment. The arrangement of the fourth embodiment can be similar to a 
fan beam scheme in X-ray CT to obtain a tomogram at high speed. 
As has been described above, according to an apparatus for measuring 
optical information of a scattering medium, and a method therefor of the 
present invention, the influence of a scattering constituent can be 
separated from the influence of an absorptive constituent, and accurate 
measurements can be performed. Optical information such as an equivalent 
scattering coefficient, an absorption coefficient, and the concentration 
of a specific constituent, spatial distributions thereof, changes in these 
pieces of optical information over time, and distributions thereof within 
a slice can be measured. In the optical information measuring apparatus 
using the present invention, use of modulated light can improve light 
utilization efficiency, and measurement accuracy can be substantially 
improved by the principle of detecting parameters such as a phase 
corresponding to a photon density wave propagating in the scattering 
medium. For these reasons, measurement, imaging, tomographic measurement, 
and the like of the above optical information of a human head, a human 
trunk, and a plant such as a tree can be performed. Therefore, the present 
invention is a remarkable invention capable of performing optical 
measurement of optical information such as the equivalent scattering 
coefficient, the absorption coefficient, and the concentration of a 
specific constituent of a scattering medium, imaging thereof, and 
tomographic measurement thereof. The present invention has great academic, 
industrial, and social influences and effects.