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The refractive index of human hemoglobin in the visible range
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2011 Phys. Med. Biol. 56 4013
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IOP PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 56 (2011) 4013–4021
doi:10.1088/0031-9155/56/13/017
The refractive index of human hemoglobin in the
visible range
O Zhernovaya1 , O Sydoruk2 , V Tuchin1 and A Douplik3,4,5
1 International Research–Educational Center of Optical Technologies for Industry and Medicine
‘Photonics’, Saratov State University, 83 Astrakhanskaya str., 410012 Saratov, Russia
2 Optical and Semiconductor Devices Group, Department of Electrical and Electronic
Engineering, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
3 Medical Photonics Engineering Group, Chair of Photonic Technologies, Friedrich-Alexander
University Erlangen-Nuremberg, Paul-Gordan-Strasse 3, 91052 Erlangen, Germany
4 Clinical Photonics Lab, SAOT Erlangen Graduate School in Advanced Optical Technologies,
Friedrich-Alexander University Erlangen-Nuremberg, Paul-Gordan-Strasse 6, 91052 Erlangen,
Germany
E-mail: [email protected]
Received 18 January 2011, in final form 11 May 2011
Published 15 June 2011
Online at stacks.iop.org/PMB/56/4013
Abstract
Because the refractive index of hemoglobin in the visible range is sensitive to the
hemoglobin concentration, optical investigations of hemoglobin are important
for medical diagnostics and treatment. Direct measurements of the refractive
index are, however, challenging; few such measurements have previously been
reported, especially in a wide wavelength range. We directly measured the
refractive index of human deoxygenated and oxygenated hemoglobin for nine
wavelengths between 400 and 700 nm for the hemoglobin concentrations up
to 140 g l−1 . This paper analyzes the results and suggests a set of model
functions to calculate the refractive index depending on the concentration.
At all wavelengths, the measured values of the refractive index depended on
the concentration linearly. Analyzing the slope of the lines, we determined the
specific refraction increments, derived a set of model functions for the refractive
index depending on the concentration, and compared our results with those
available in the literature. Based on the model functions, we further calculated
the refractive index at the physiological concentration within the erythrocytes
of 320 g l−1 . The results can be used to calculate the refractive index in the
visible range for arbitrary concentrations provided that the refractive indices
depend on the concentration linearly.
(Some figures in this article are in colour only in the electronic version)
5
Author to whom any correspondence should be addressed.
0031-9155/11/134013+09$33.00
© 2011 Institute of Physics and Engineering in Medicine
Printed in the UK
4013
4014
O Zhernovaya et al
1. Introduction
A part of a standard complete blood count is to determine the total hemoglobin concentration,
the hematocrit, and the mean corpuscular hemoglobin. Independent optical methods of
evaluating these blood parameters help develop quality control of blood analysis. Among these
methods, measurements of the refractive index and the absorption of blood are routinely used
for exact determination and monitoring of hemoglobin concentration (van Kampen and Zijlstra
1965, Fabry and Old 2009). One of the important applications is monitoring of hemolysis
when hemoglobin leaks out from erythrocytes and, consequently, the local concentration of
hemoglobin rapidly changes. Blood optics is also important for biophotonic and clinical
applications, both in therapy and diagnostics.
Light absorbing and scattering properties of blood depend on the refractive index
of erythrocytes, which is mainly determined by the concentration of hemoglobin in
erythrocytes. The major source of scattering in blood is the refractive-index mismatch
between erythrocytes and blood plasma. High-accuracy measurements of the refractive
and the spectral properties of hemoglobin facilitate monitoring and modification of the
optical properties of blood and blood-containing tissues and improve optical immersion
methods exploited in existing optical diagnostic and therapeutical techniques, such as
optical coherence tomography, reflectance spectroscopy, photodynamic therapy, and laser
surgery.
The refractive index of hemoglobin is a complex value. Its imaginary part was described
by absorption measurements and thoroughly tabulated for wavelengths between 250 and
1000 nm (Prahl 1999). On the other hand, measuring the real part of the refractive index is
challenging, especially in a wide wavelength range. In 1957, Barer (1957) determined the real
part of the refractive index of hemoglobin at a single wavelength of 589 nm, and his result has
been actively used ever since, see e.g. Friebel and Meinke (2005, 2006), Rappaz et al (2008).
Barer’s expression assumes that the real part of the refractive index, n, is proportional to the
hemoglobin concentration, C
n = nH2 O + αC,
(1)
where nH2 O is the refractive index of distillate water and α is the specific refraction
increment.
Recently, the refractive index within the visible and near-infrared range has been found
by applying Kramers–Kronig relations (Faber et al 2004) and by simultaneous measurements
of both specular reflection and light absorption spectra (Friebel and Meinke 2005, 2006).
Both methods are indirect and rely on the imaginary part of the refractive index for
calculating the real part. The reported values of the refractive index vary across publications.
Moreover, most of the previous measurements of the refractive index have been carried
out for the oxygenated form of hemoglobin. In blood, however, hemoglobin is present
both in the oxygenated and in the deoxygenated forms, and, therefore, both forms must be
studied.
Using a refractometer based on the total internal reflection, we directly measured the real
part of the refractive index of deoxygenated and oxygenated hemoglobin at nine wavelengths
between 400 and 700 nm. Changing the concentration of the hemoglobin, we could determine
specific refraction increments at these wavelengths assuming that the refractive index depends
on the concentration linearly. Section 2 describes the preparation of the materials and the
measurements. Section 3 presents the results of the measurements and the model functions
we propose to describe the specific refraction increments. It also compares our results with
those given in earlier publications. Section 4 draws conclusions.
The refractive index of human hemoglobin
Table 1.
37 ◦ C.
4015
The refractive index of water and methemoglobin at temperatures of 20
◦C
and
Wavelength (nm)
401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5
n(water), 20 ◦ C
n(water), 37 ◦ C
n(metHb), 20 ◦ C
n(metHb), 37 ◦ C
1.343
1.341
1.345
1.343
1.340
1.338
1.342
1.341
1.337
1.335
1.339
1.338
1.334
1.332
1.337
1.335
1.333
1.331
1.335
1.333
1.333
1.331
1.335
1.333
1.332
1.330
1.334
1.332
1.332
1.329
1.333
1.332
1.330
1.328
1.332
1.330
2. Materials and methods
The digital multiwavelength refractometer DSR-λ (Schmidt&HaenschTM , Germany) used in
our experiments measures refractive indices at nine wavelengths: 401.5, 435.8, 486.1, 546.1,
587.6, 589.3, 632.8, 656.3 and 706.5 nm, covering the entire visible range. The refractometer is
designed to measure the refractive index of highly absorbing and non-translucent substances,
particularly suitable for high-concentration hemoglobin solutions. The refractive index is
determined from the measurements of the angle of total internal reflection.
Human hemoglobin (lyophilized powder) obtained from Sigma-Aldrich was dissolved in
phosphate buffered saline (PBS) to maintain pH at 7.4 and exclude changes of the refractive
index due to changes of the pH value. The refractive index of PBS is about 0.002 higher
than the refractive index of water at all wavelengths. Dry hemoglobin was in the form
of methemoglobin. To obtain solutions of deoxygenated and oxygenated hemoglobin with
the concentrations of 0–140 g l−1 , sodium dithionite and sodium bicarbonate, respectively,
were added to all samples (Dalziel and O’Brien 1961). The optimal concentration of sodium
dithionite for full conversion of methemoglobin to the deoxygenated hemoglobin was found to
be 10 g l−1 . To convert methemoglobin to oxygenated hemoglobin, sodium bicarbonate with
the concentration of 15 g l−1 was used. Addition of sodium dithionite and sodium bicarbonate
increased the overall refractive index of hemoglobin solution. When the amount by which
the refractive index increased was subtracted, the refractive index of both deoxygenated and
oxygenated hemoglobin became almost equal to the refractive index of the methemoglobin
initial solution. One can assume that the chemical interaction between hemoglobin and the
solutions of sodium dithionite and sodium bicarbonate does not lead to a considerable change
of the refractive index of hemoglobin, and therefore, the increase of the refractive index of the
hemoglobin solution due to sodium dithionite and sodium bicarbonate can be neglected.
The values of the refractive index of water measured at the nine wavelengths are given in
table 1. They are in good agreement with data presented by other authors, see e.g. Thormahlen
et al (1985). The measurement error was estimated experimentally for multiple preparations of
samples. The absolute measurement error was calculated and its average value did not exceed
0.001. In addition, the sample-layer thickness did not influence noticeably the measured
values of the refractive index.
For most of our measurements, we stabilized the temperature of the samples inside the
refractometer at 20 ◦ C to minimize evaporation of water in the sample chamber. We have,
however, also estimated the temperature dependence of the refractive index of hemoglobin for
the hemoglobin solution with a concentration of about 0.5 g l−1 . Dry hemoglobin (lyophilized
powder) was in the form of methemoglobin. As the measurements showed, methemoglobin
had the same refractive index as oxygenated and deoxygenated hemoglobin at the wavelengths
beyond the regions of anomalous dispersion, in the range of 487–707 nm. The refractive index
4016
O Zhernovaya et al
Table 2. The refractive index of deoxygenated hemoglobin (Hb), measured at different wavelengths
and for different values of the concentration. The measurements at zero concentration correspond
to the pure solvent (phosphate buffered saline).
Wavelength (nm)
Concentration (g/l) 401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5
0
20
30
40
50
60
70
80
90
100
110
120
130
140
1.345
1.349
1.350
1.351
1.353
1.354
1.355
1.357
1.359
1.360
1.362
1.363
1.365
1.365
1.342
1.347
1.348
1.350
1.352
1.354
1.355
1.357
1.359
1.360
1.363
1.364
1.366
1.367
1.339
1.343
1.345
1.346
1.348
1.349
1.350
1.352
1.354
1.355
1.357
1.358
1.360
1.361
1.336
1.340
1.342
1.343
1.345
1.346
1.347
1.349
1.350
1.352
1.354
1.355
1.356
1.357
1.335
1.339
1.340
1.342
1.343
1.345
1.346
1.348
1.349
1.350
1.352
1.353
1.355
1.356
1.335
1.339
1.340
1.342
1.343
1.345
1.346
1.348
1.349
1.350
1.352
1.353
1.355
1.356
1.334
1.337
1.339
1.341
1.342
1.343
1.344
1.346
1.347
1.349
1.350
1.352
1.353
1.354
1.333
1.337
1.338
1.340
1.341
1.343
1.344
1.345
1.347
1.348
1.350
1.351
1.353
1.354
1.332
1.336
1.337
1.338
1.340
1.341
1.342
1.344
1.345
1.347
1.348
1.350
1.351
1.352
of the methemoglobin solution and water was measured for temperatures of 20 ◦ C and 37 ◦ C
(table 1). The refractive index of hemoglobin at 37 ◦ C is about 0.001–0.002 lower than that at
20 ◦ C for all wavelengths. In addition, the refractive indices of water at these two temperatures
differ by 0.002. It can, therefore, be assumed that the refractive index of hemoglobin solutions
at various temperatures is influenced mainly by the refractive index of water in which it is
dissolved.
3. Results
Tables 2 and 3 show the values of the refractive index measured for the deoxygenated and
oxygenated hemoglobin, respectively. When plotted against the concentration, the values of
the refractive index at different wavelengths (circles in figure 1) fit into straight lines. We
assumed that the lines are determined by an equation similar to (1):
n = n0 + αC,
(2)
where α is, as above, the specific refraction increment and n0 is the ‘effective’ refractive index at
zero concentration. At each wavelength, we then determined the values of α and n0 by the linear
least-squares method using the Matlab function ‘polyfit’. These values are given in table 4
and the corresponding lines are plotted in figure 1. For the whole concentration range, the
calculated lines agree with the measured values within the experimental error (0.001).
For the deoxygenated hemoglobin, figure 1(a), the slope of the line at 402 nm is smaller
than that of the line at 436 nm, indicating a region of anomalous dispersion matching the
Soret band of deoxygenated hemoglobin (432–434 nm) (Prahl 1999). For the deoxygenated
hemoglobin, however, we observed normal dispersion at all wavelengths, see figure 1(b).
For a detailed comparison between the refractive indices of oxygenated and deoxygenated
hemoglobin, we plot in figure 2(a) the values measured at the concentration of 100 g l−1 .
There is almost no difference between refractive indices of deoxygenated and oxygenated
The refractive index of human hemoglobin
4017
Table 3. The refractive index of oxygenated hemoglobin (HbO2 ), measured at various wavelengths
and different values of concentration. The measurements at zero concentration correspond to the
pure solvent (phosphate buffered saline).
Wavelength (nm)
Concentration (g/l) 401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5
0
20
30
40
50
60
70
80
90
100
110
120
130
140
1.345
1.349
1.350
1.352
1.354
1.355
1.357
1.359
1.360
1.362
1.364
1.366
1.367
1.369
1.342
1.347
1.348
1.350
1.351
1.353
1.354
1.356
1.358
1.359
1.361
1.362
1.364
1.366
1.339
1.343
1.345
1.346
1.348
1.349
1.350
1.352
1.353
1.355
1.356
1.358
1.359
1.361
1.336
1.340
1.342
1.343
1.345
1.346
1.347
1.349
1.350
1.352
1.353
1.355
1.356
1.357
1.335
1.339
1.340
1.342
1.343
1.345
1.346
1.348
1.349
1.350
1.352
1.353
1.354
1.357
1.335
1.339
1.340
1.342
1.343
1.344
1.346
1.348
1.349
1.350
1.352
1.353
1.354
1.357
1.334
1.338
1.339
1.340
1.342
1.343
1.344
1.346
1.347
1.349
1.350
1.352
1.353
1.355
1.333
1.337
1.338
1.340
1.341
1.342
1.344
1.345
1.347
1.348
1.350
1.351
1.352
1.354
1.332
1.336
1.337
1.339
1.340
1.341
1.342
1.344
1.345
1.347
1.348
1.350
1.351
1.352
Table 4. The effective refractive indices at zero concentration and the specific refraction increments
for the deoxygenated (Hb) and oxygenated hemoglobin (HbO2 ) as determined from the slope of
the curves in figure 1.
Wavelength (nm)
401.5 435.8 486.1 546.1 587.6 589.3 632.8 656.3 706.5
n0
1.345 1.343 1.340 1.337 1.336 1.336 1.334 1.334 1.330
0.146 0.177 0.154 0.148 0.147 0.147 0.144 0.146 0.140
α, Hb (ml g−1)
α, HbO2 (ml g−1) 0.170 0.163 0.150 0.150 0.147 0.148 0.144 0.145 0.143
hemoglobin between 486 and 707 nm. There is a difference, however, at 402 and 436 nm,
which can be explained by different positions of the Soret bands of deoxygenated and
oxygenated hemoglobin. Compared with the Soret peak of deoxygenated hemoglobin, the
Soret peak of oxygenated hemoglobin is shifted to the ultraviolet region. The anomalous
dispersion in this region determines the behavior of the refractive index of deoxygenated
hemoglobin. Our measurements, therefore, do not show any significant difference between
deoxygenated and oxygenated hemoglobin in the visible range for the wavelengths away from
the Soret absorption bands.
The linear dependence between the refractive index and the concentration (2) is valid not
only in the concentration range used in our experiments but also for higher concentrations
(Friebel and Meinke 2006). We experimentally observed such a linear dependence for solutions
of methemoglobin in water with the hemoglobin concentrations up to 280 g l−1 . Figure 2(b)
shows the spectrum of refractive indices at 320 g l−1 , which corresponds to the physiological
concentration of hemoglobin within the erythrocytes, calculated using (2) and the values from
table 4. The region of anomalous dispersion due to the Soret band of the deoxygenated
hemoglobin (orange circles and line in figure 2) can be clearly seen. On the other hand, the
change of the refractive index due to the Q-band (with the maximum at 556 nm) is almost
4018
O Zhernovaya et al
(a)
(b)
Figure 1. The measured values of the refractive index (dots) depend linearly on the concentration
at all wavelengths both for (a) deoxygenated and (b) oxygenated hemoglobin. The black lines are
calculated using the least-squares method. From the slope of the lines, we determined the specific
refraction increments (see table 4) from (2).
indistinct. Instead, anomalous dispersion is seen for deoxygenated hemoglobin between 633
and 656 nm, but because the difference between the corresponding values of the refractive
index is only 0.001, it can be attributed to experimental error. For oxygenated hemoglobin
(black circles and lines in figure 2), the dispersion is normal for the whole wavelength
range. The values of the refractive indices of oxygenated and deoxygenated hemoglobin differ
considerably only at 402 and 436 nm, and they differ little from each other for the rest of
the wavelength range, in agreement with the behavior at lower concentrations (compare with
figure 2(a)).
We will now compare our results with those available in the literature. At the wavelength
of 589 nm and the concentration of 320 g l−1 , our calculated value of the refractive index
is 1.383 for both hemoglobins, whereas the value given by Friebel and Meinke (2006) for
oxygenated hemoglobin is 1.418 and that given by Barer (1957) is 1.394. Our value is lower
than the other two, although the difference between our and Barer’s results, 0.011, is two
times smaller than the difference between the results of Barer and Friebel and Meinke (0.024).
Barer’s value for the specific refraction increment is 0.193 ml g−1 , whereas our value for the
oxygenated hemoglobin is 0.147 ml g−1 . For the hemoglobin concentration of 64.5 g l−1 at
25 ◦ C, Jin et al (2006) reported the value of the refractive index of 1.335 at 632.8 nm, whereas
our value is about 1.343 at the same wavelength. At 633 nm, Friebel and Meinke measured
the refractive index of 1.360 for the hemoglobin solution with the concentration of 104 g l−1
The refractive index of human hemoglobin
4019
(a)
(b)
Figure 2. (a) Measured values of the refractive index of deoxygenated (Hb, orange), and
oxygenated (HbO2 , black) hemoglobin for the concentration of 100 g l−1 . (b) Refractive index for
the deoxygenated and oxygenated hemoglobin at a concentration of 320 g l−1 calculated using the
model functions. The lines serve as a guide for the eyes.
(Friebel and Meinke 2006). This value is 0.011 higher than our results for the hemoglobin
concentration of 100 g l−1 at 632.8 nm (see tables 2 and 3). Faber et al (2004) measured the
refractive index of oxygenated and deoxygenated hemoglobin solutions at 800 nm as 1.392
for oxygenated hemoglobin and 1.388 for deoxygenated hemoglobin with the concentration
of 93 g l−1 . Their difference of 0.004 between the refractive indices of oxygenated and
deoxygenated hemoglobin is much larger than would be expected from our measurement.
Moreover, the values obtained by Faber et al are much higher than our results: our refractive
measurements give 1.347 for both oxygenated and deoxygenated hemoglobin at 706.5 nm for
the concentration of 100 g l−1 .
As can be seen, our results differ from those reported in the literature at various wavelength
and concentrations. There is, however, no agreement also between the earlier results. The
discrepancy between different experiments can be due to different methods of extracting
hemoglobin from fresh blood samples. In contrast, we have used hemoglobin prepared from
a commercially available chemical reagent. The advantage of this method is that it allows us
to obtain reproducible results that could be compared between different research groups.
Our results could be useful for estimating the refractive index of blood and hemoglobin in
erythrocytes. The concentration of hemoglobin inside erythrocytes is 250–350 g l−1 (Meinke
et al 2011). Hemoglobin in erythrocytes is dissolved in intracellular fluid supposed to have
a higher refractive index than that of water (for example, the refractive index of cytoplasm is
about 1.350–1.367 at the wavelengths of 400–700 nm (Duck 1990)). Our calculations for the
hemoglobin concentration of 320 g l−1 (as it is in erythrocytes) give the value of the refractive
4020
O Zhernovaya et al
index of about 1.380 for the wavelengths in the range of 600–700 nm. Inside erythrocytes,
hemoglobin at this concentration is supposed to have the refractive index value slightly higher
than 1.380 due to the contribution of the refractive index of the intracellular medium.
Human whole blood consists of about 40–45% erythrocytes and 55–60% plasma. The
refractive index of blood plasma varies from 1.358 at 400 nm to 1.344 at 700 nm (Cheng et al
2002, Meinke et al 2011). The membrane of erythrocyte has a slightly higher refractive index
than plasma (Barer 1957), and the refractive index of erythrocyte is mainly determined by the
hemoglobin concentration inside the erythrocyte. The refractive index of whole blood can be
estimated using the Gladstone–Dale equation (Fikhman 1967)
nblood = ne Ve + np Vp ,
(3)
where ne and np are the refractive indices of erythrocytes and plasma, respectively, and Ve and
Vp are the corresponding volume fractions.
Because experiments in the field of tissue optics are often being done in the near-infrared
region, estimating the refractive index of hemoglobin in this range could be important for
practical applications. Although our measurements were done in the visible range, the
wavelength dependence of the refractive index can be extrapolated to the near-infrared region
as there are no noticeable absorption peaks in this region and, consequently, anomalous
dispersion do not influence significantly on index values (Friebel and Meinke 2005).
4. Conclusions
The measured values of the refractive index cover the whole visible range. As our results
indicate, there are no significant differences between the refractive index of deoxygenated
and oxygenated hemoglobin in the visible range for the wavelengths beyond the regions of
anomalous dispersion. Being directly measured, our results can be used for cross validation
of results obtained by indirect methods. In particular, they can serve for resolving the
controversy of using the Kramers–Kronig relations to obtain the real part of the refractive
index of hemoglobin from its imaginary part or absorption spectra (Faber et al 2004, Friebel
and Meinke 2005). The model functions derived can be used to determine the refractive index
for arbitrary values of the concentration within the range where equations (1) and (2) are valid.
This range includes the physiological concentration of hemoglobin both in blood (140 g l−1 )
and in erythrocytes (320 g l−1 ), which shows the potential of the model functions for clinical
applications.
Acknowledgments
OZ and AD acknowledge funding of the Erlangen Graduate School in Advanced Optical
Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of
the Excellence initiative. VT and OZ were partly supported by grant PHOTONICS4LIFE-FP7ICT-2007-2 and the governmental contracts of the RF 02.740.11.0770 and 02.740.11.0879.
References
Barer R 1957 Refractometry and interferometry of living cells J. Opt. Soc. Am. 47 545–56
Cheng S, Shen H Y, Zhang G, Huang C H and Huang X J 2002 Measurement of the refractive index of biotissue at
four laser wavelengths Proc. SPIE 4916 172–6
Dalziel K and O’Brien J R P 1961 The kinetics of deoxygenation of human haemoglobin Biochem. J. 78 236–45
Duck F A 1990 Physical Properties of Tissue: A Comprehensive Reference Book (London: Academic)
The refractive index of human hemoglobin
4021
Faber D J, Aalders M C G, Mik E G and Hooper B A 2004 Oxygen saturation-dependent absorption and scattering
of blood Phys. Rev. Lett. 93 028102
Fabry M and Old J M 2009 Laboratory methods for diagnosis and evaluation of hemoglobin disorders Disorders of
Hemoglobin ed M H Steinberg et al (Cambridge: Cambridge University Press) chapter 28, pp 656–86
Fikhman B A 1967 Microbiological Refractometry (Moscow: Medicine)
Friebel M and Meinke M 2005 Determination of the complex refractive index of highly concentrated hemoglobin
solutions using transmittance and reflectance measurements J. Biomed. Opt. 10 064019
Friebel M and Meinke M 2006 Model function to calculate the refractive index of native hemoglobin in the wavelength
range of 250–1100 nm dependent on concentration Appl. Opt. 45 2838–42
Jin Y L, Chen J Y, Xu L and Wang P N 2006 Refractive index measurement for biomaterial samples by total internal
reflection Phys. Med. Biol. 51 371–9
Meinke M C, Friebel M and Helfmann J 2011 Optical properties of flowing blood cells Advanced Optical Flow
Cytometry: Methods and Disease Diagnoses ed V V Tuchin (Weinheim: Wiley-VCH) chapter 5, pp 95–129
Prahl S A 1999 http://omlc.ogi.edu/spectra/hemoglobin/index.html
Rappaz B, Barbul A, Emery Y, Korenstein R, Depeursinge C, Magistretti P J and Marquet P 2008 Comparative
study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume
analyzer Cytometry A 73 895–903
Thormahlen I, Straub J and Grigull U 1985 Refractive index of water and its dependence on wavelength, temperature
and density J. Phys. Chem. Ref. Data 14 933–45
van Kampen E J and Zijlstra W G 1965 Determination of hemoglobin and its derivatives Adv. Clin. Chem. 8 141–87