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Measurement of six parameters (LB/CB and LD/CT)
Figure 6.1 presents a schematic illustration of the experimental setup used to verify the performance of the proposed analytical model In performing the experiments, the input light was provided by a frequency-stable He-Ne laser (SL 02/2, SIOS Co.) with a central wavelength of 632.8 nm In addition, a polarizer (GTH5M, Thorlabs Co.) and quarter-wave plate (QWP0-633-04-4-R10, CVI Co.) were used to produce four linear polarization lights (0°, 45°, 90° and 135°) and two circular polarization lights (right-handed and left-handed) A neutral density filter (NDC-100-2, ONSET Co.) and power meter detector (8842A, OPHIT Co.) were used to ensure that each of the input polarization lights had an identical intensity. Note that for samples with no linear dichroism, the output Stokes parameters can be normalized as Sc/So since the terms m2, m73 and mz4 in Eq (4) are non-zero Thus, there is no need to ensure that the six input lights have an identical optical intensity before entering the sample However, for samples with linear dichroism, the output Stokes parameters cannot be normalized in this way, and thus the neutral density filter and power meter detector are required.
The output Stokes parameters were computed from the intensity measurements obtained using a commercial Stokes polarimeter (PAX5710, Thorlabs Co.) at a sampling rate of 30 samples per second A minimum of 1024 data points were obtained for the effective parameters (a, B, 0a, D, y and R) of each sample Of these data points, 100 points were then chosen in order to calculate the mean value of each parameter.
Figure 6.1 Schematic diagram of the measurement system for characterizing an LB/CB and LD/CD of an optical sample.
The validity of the proposed measurement method was evaluated using different optical samples, namely a quarter-wave plate (QWP0-633-04-4-R10, CVI Co.), a half-wave plate (QWP0-633-04-2-R10, CVI Co.), the de-ionized water with containing D-glucose, a polarizer (GTH5SM, Thorlabs Co.), a polarization controller, and a polymer polarizer (LLC2-82-18S, OPTIMAX Co.) baked in an oven at 150°C for 100 minutes Also, a composite sample comprising a quarter-wave plate, a half-wave plate and a polarizer in aligned or non-aligned principal axis were tested.Note that the polarization controller was used to evaluate the performance of the proposed method in extracting the parameters of samples with circular dichroism only Meanwhile, the baked polarizer was chosen in order to evaluate the performance of the proposed method in measuring the optical parameters of samples with both linear birefringence and linear dichroism.
Measurement of nine parameters (LB/CB, LD/CD and depolarization)
Figure 6.2 presents a schematic illustration of the experimental setup proposed in this study for characterizing the LB, LD, CB, CD, L-Dep, and C-Dep properties
104 of a turbid media In performing the experiments, the input light was provided by a frequency-stable He-Ne laser (SL 02/2, SIOS Co.) with a central wavelength of 632.8 nm In addition, a polarizer (GTH5M, Thorlabs Co.) and quarter-wave plate (QWP0-633-04-4-R10, CVI Co.) were used to produce four linear polarization lights (0°, 45°, 90° and 135°) and two circular polarization lights (right-handed and left-handed) A neutral density filter (NDC-100-2, ONSET Co.) and power meter detector (8842A, OPHIT Co.) were used to ensure that each of the input polarization lights had an identical intensity Note that for samples with no dichroism, the output Stokes parameters can be normalized as Sc /So since the terms my2, m¡3 and ím;x in Eq (3) are non-zero Thus, there is no need to ensure that the six input lights have an identical optical intensity before entering the sample. However, for samples with dichroism, the output Stokes parameters cannot be normalized in this way, and thus the neutral density filter and power meter detector are required.
The output Stokes parameters were computed from the intensity measurements obtained using a commercial Stokes polarimeter (PAX5710, Thorlabs Co.) at a sampling rate of 30 samples per second A minimum of 1024 data points were obtained for the effective parameters (a, B, 84, D, y R, e1, e2, and e3) of each sample.
Of these data points, 100 points were then chosen in order to calculate the mean value of each parameter.
| lo LD CB LB C-Dep L-Dep ry h
Figure 6.2 Schematic illustration of experimental measurement system.
The validity of the proposed measurement method was evaluated using six different optical samples, namely a polarizer (LLC2-82-18S, OPTIMAX Co.) baked in an oven at a temperature of 150°C for 100 minutes; two different diameters suspended particles (polystyrene microspheres) with containing glucose; de-ionized water with containing D-glucose; a depolarizer; and a composite sample comprising of a depolarizer and a quarter-wave plate It is noted that the polarizers used in the tested samples for baking are polymer polarizers The baked polarizer was chosen to evaluate the performance of the proposed measurement system in measuring the optical parameters of samples with both linear birefringence and linear dichroism properties, respectively Meanwhile, two different diameters suspended particles and de-ionized water with containing D-glucose were chosen in order to evaluate the performance of the proposed method in measuring the optical parameters of turbid media with circular birefringence Moreover, the depolarizer was chosen in order to evaluate the performance of the proposed measurement system in extracting the optical parameters of sample with depolarization Finally, the composite sample was chosen in order to evaluate the performance of the proposed measurement system in extracting the optical parameters of turbid media with linear birefringence and depolarization, respectively.
Experimental results 55 < 5< se s9 8950896085885 86 111
Experimental results of six parameters (LB/CB and LD/CD)
The validity of the proposed measurement method was evaluated using different optical samples, namely a quarter-wave plate (QWP0-633-04-4-R10, CVI Co.), a half-wave plate (QWPO0-633-04-2-R10, CVI Co.), the de-ionized water with containing D-glucose, a polarizer (GTH5M, Thorlabs Co.), a polarization controller, and a polymer polarizer (LLC2-82-18S, OPTIMAX Co.) baked in an oven at 150°C for 100 minutes Also, a composite sample comprising a quarter-wave plate, a half-wave plate and a polarizer in aligned or non-aligned principal axis were tested. Note that the polarization controller was used to evaluate the performance of the proposed method in extracting the parameters of samples with circular dichroism only Meanwhile, the baked polarizer was chosen in order to evaluate the performance of the proposed method in measuring the optical parameters of samples with both linear birefringence and linear dichroism.
7.1.1 Quarter-wave plate (LB only)
Figure 7.1 illustrates the experimental results obtained for the effective properties of the quarter-wave plate (QW) From inspection, the standard deviations of the orientation angle and phase retardance measurements are found to be just 0.04° and 0.013°, respectively In other words, the ability of the proposed method to extract the properties of samples with linear birefringence only is confirmed As expected, the linear dichroism, optical rotation angle and circular dichroism parameters have a value close to zero at all values of the orientation angle As
111 discussed in Section 4.3, the proposed analytical model yields reliable results for the orientation angle of LD only for samples with a linear dichroism greater than or equal to 0.05 In the present sample, the linear dichroism is close to zero, and thus the orientation angle of LD varies randomly in the range of 0° ~ 180° as the orientation angle of LB is increased (see Figure 7.1(b)) As expected, Figs 7.1 (c) and 7.1 (d) show that the optical rotation angles and values of circular dichroism of the quarter-wave plate are also close to zero.
('Bop) uoIyep1e1o1 oseud peInseoI NO oO “0.2 for) Oo Q =) © an a wslouyolp 1E@UI| DoInsee|0| œ © œ oO T
Measured orientation angle of LB (deg Oo Measured orientation angle of LD (deg oO oO
Known principal axis of QW (deg.) Known principal axis of QW (deg.)
Measured optical rotation (deg.) BN 63 to an 7 Measured circular dichroism oO Ooœ ES ° ° io 7
Known pinopa Ai of QW (deg.) Known principal ays of QW (deg.) c
Figure 7.1 Experimental results for effective parameters of quarter-wave plate (QW).
7.1.2 Hal-wave plate and de-ionized water containing D-glucose (CB only)
7.1.2.1 Half-wave plate (CB property only)
In general, the elements in the Mueller matrix for an optically active material are different from those in the Mueller matrix for a half-wave plate The Mueller matrix of a half-wave plate with an optical rotation yy has the form as
Thus, in computing the optical rotation angle of the half-wave plate, the formula of linear retardance () is revised as:
Then, the formula of optical rotation (y) is revised as:
2 Ay, ~ As; or y= ! tan” tae a (7.1.5)
Figure 7.2 presents the experimental results for the effective properties of the half-wave plate Figure 7.2(c) shows that a good agreement is obtained between the measured value of the optical rotation angle and the actual value of the optical rotation angle over the considered range of 0~90° From inspection, the standard deviation of the optical rotation angle is found to be just 0.008° As discussed in
Section 3.3, the analytical model yields reliable results for the orientation angle of
LB only for samples with a phase retardance greater than or equal to 3° Similarly, reliable results for the orientation angle of LD are obtained only for samples with a linear dichroism greater than or equal to 0.05 Figures 7.2(a) and 7.2(b) show that both the retardance and the linear dichroism of the half-wave plate are close to zero. Thus, the extracted values of the orientation angle of LB and orientation angle of
LD vary randomly as the optical rotation angle is increased As expected, Figure 7.2(d) shows that the circular dichroism of the half-wave plate is also close to zero.
Known Principe "` of HP (deg.) Known Princip of HP (deg.) a
Known principal axis of HP (deg.) Known principal axis of HP (deg.)
Figure 7.2 Experimental results for effective parameters of half-wave plate (HP).
7.1.2.2 De-ionized water containing D-glucose (CB property only)
Figure 7.3 illustrates the experimental results obtained for the effective parameters of the de-ionized water with containing D-glucose (Merck Ltd.) The D-glucose was poured into a container of de-ionized water The average measured values of the optical parameters of the sample with different concentration of glucose from 0 ~ 1M (Molar) in increments of 0.1M are summarized The container is glass and its width is 12.5mm outside and 10mm inside Distance from center of sample to surface of detector is 23mm Figure 7.3(c) shows the measured value of the optical rotation angle regarding to the concentration of glucose over the considered range of 0 ~ 1M The sensitivity of the D-glucose measurement is estimated 1.9 mol/l, and it is a good agreement with [134] From inspection, the standard deviation of the optical rotation angle is found to be just 0.01° As discussed in Section 3.3, the analytical model yields reliable results for the orientation angle of LB only for samples with a phase retardance greater than or equal to 3° Similarly, reliable results for the orientation angle of LD are obtained only for samples with a linear dichroism greater than or equal to 0.05 Figures 7.3(a) and 7.3(b) show that both the retardance and the linear dichroism of the de-ionized water with containing D-glucose are close to zero Thus, the extracted values of the orientation angle of LB and orientation angle of LD vary randomly as the concentration of glucose is increased As expected, Figure 7.3(d) shows that the circular dichroism of the de-ionized water with containing D-glucose is also close to zero.
= m @ oe oO n c = Đ 80 155 ỉ 90 0.153 bì a 2 bị bị a oo 2 ® 75° 1 8 § 60 19
Concentration of glucose (M) Concentration of glucose (M)
Figure 7.3 Experimental results for effective parameters of de-ionized water with containing D-glucose.
Figure 7.4 presents the experimental results for the effective parameters of the polarizer As expected, the linear dichroism has a value close to one (see Figure 7.4(b)) Moreover, a good agreement is observed between the measured values of the orientation angle of LD and the known values From inspection, the standard deviations of 64 and D are found to be just 0.007° and 1.42x10%, respectively In other words, the ability of the proposed analytical model to extract the parameters of samples with pure LD properties is confirmed Figures 7.4(c) and 7.4(d) confirm that the CB and CD properties of the polarizer are close to zero As discussed in Section 3.3, reliable results are obtained for the orientation angle of LB provided that the phase retardance has a value greater than or equal to 3° As shown in Figure
7.4(a), the polarizer has a retardance of less than 2° Thus, the extracted value of the orientation angle of LB varies randomly in the range of 0 ~ 180° as the orientation angle of LD is increased Note that in previous studies by the current group [103,
104], both the retardance and the orientation angle of LB of the polarizer were found to vary randomly with the orientation angle of LD However, in the present study, the extracted value of the retardance is approximately constant In other words, the decoupled nature of the analytical model proposed in this study successfully resolves the “multiple solutions” problem found in [103, 104] for samples with a linear dichroism of D=1.
(Bap) uoIepIeo1 aseyd pe1nseeIn| = no oO T ơ ơ
Measured orientation angle of LB
Known principal axis of P (deg.) Known principal axis of P (deg.)
Known principal axis of P (deg.) Known principal axis of P (deg.)
Figure 7.4 Experimental results for effective parameters of polarizer (P).
In the present study, a sample with pure CD properties was simulated using a polarization controller comprising a half-wave plate sandwiched between two quarter-wave plates and a neutral density filter (NDF) In performing the measurement process, the experimental settings of the polarization controller and NDF required to replicate a pure CD sample were determined using the genetic algorithm (GA) method described in [126, 127] That is, having specified the desired value of the circular dichroism (e.g., R=0.2), the orientation angle of the two quarter-wave plates (ơi and 2), the optical rotation angle of the half-wave plate (yi), and the output intensity of the NDF were tuned in accordance with the results obtained from the GA such that the following condition was satisfied for each of the six input polarization lights.
5, = LM oy IM pe IM ow 2 ILM yop IS, ~ IMIS, (7.1.6) where S, are the output Stokes parameters obtained when using the simulated CD sample, [Maw] and [Mowz] are the Mueller matrices of the two quarter-wave plates, [Mup] is the Mueller matrix of the half-wave plate, [Mnpr] is the Mueller matrix of the neutral density filter, and [Mca] is the theoretical Mueller matrix of a sample with CD properties only Six different values of ơi, da, y¡, and the NDF output intensity were obtained for input lights of Soằ, Suse, Sooe, Sisse, SRHc, and Stuc, respectively In performing the experiments, the polarization controller and NDF were set accordingly, and the resulting output Stokes parameters were measured using a commercial polarimeter (PAX5710, Thorlabs Co.) The circular dichroism of the simulated sample was then calculated using Eq (4.3.16) in Section 3.3.
Figure 7.5(d) shows that a good agreement is obtained between the measured values of the circular dichroism and the simulated values From inspection, the standard deviation of the measured values is just 2.94x10~“ Thus, the ability of the proposed method to extract the parameters of an optical sample with CD properties
118 only is confirmed As expected, Figure 7.5(b) shows that the linear dichroism of simulated sample is close to zero Thus, the extracted values of the orientation angle of LD vary randomly as the simulated circular dichroism value is increased. Note that for a sample with pure CD properties, the phase retardance and optical rotation angle are very small (zero, ideally) However, the polarization controller and NDF do not provide sufficient parameters for the actual LB and CB properties of the simulated sample to be explored As shown in Figs 7.5(a) and 7.5(c), the extracted value of the orientation angle and the linear retardance of LB and the optical rotation of CB varies randomly in the range of 0 ~ 180° as the simulated circular dichroism value is increased.
Input circular dichroism value Input circular dichroism value
Input 210 ỹmosm value Input imal eel value c
Figure 7.5 Experimental results obtained for effective parameters of simulated CD sample.
7.1.5 Baked polarizer (LB and LD properties)
Figure 7.6 illustrates the experimental results obtained for the LB and LD properties of the baked polarizer (BP) As expected, the measured values of the optical rotation angle and circular dichroism are close to zero (see Figs 7.6(c) and 7.6(d)) Due to the prolonged exposure of the polarizer to a high-temperature environment, the input light leaks through one of the LD axes Thus, as shown in Figure 7.6(b), the linear dichroism has a value close to 1 Moreover, it can be seen that a good agreement exists between the measured values of the orientation angle of LD and the given values The average value of the phase retardance is found to be 16.92° (see Figure 7.6(a)) In addition, a good correlation is observed between the measured values of the orientation angle of LB and the given values From inspection, the standard deviations of the extracted values of a, B, Đ¿ and D are found to be just 0.03°, 0.03°, 0.01° and 4.16x10, respectively In other words, the proposed analytical model enables the parameters of hybrid samples with both LB and LD properties to be accurately determined.
60- are fo) ° i=) ° © WSIOJYoIp 1E@UI| pounseay| wo © a N (‘6ap) uoIyepIee1 eseud peInseoI w is} ° Ẳœ
Measured orientation angle of LB (deg.) oOo Measured orientation angle of LD (deg oOo = an =
Known principal axis of BP (deg.) Known principal axis of BP (deg.)
Known principal axis of BP (deg.) Known principal axis of BP (deg.)
Figure 7.6 Experimental results obtained for effective parameters of baked polarizer (BP).
7.1.6 Composite sample comprising quarter-wave plate, half-wave plate and polarizer (LB, CB and LD properties)
7.1.6.1 Aligned principal axis of quarter-wave plate, half-wave plate and polarizer
Figure 7.7 shows the experimental results obtained for a composite sample comprising a polarizer (LD), a half-wave plate (CB) and a quarter-wave plate (LB).
Experimental results of nine parameters (LB/CB, LD/CD and depolarization)
The validity of the proposed measurement method was evaluated using six different optical samples, namely a polarizer (LLC2-82-18S, OPTIMAX Co.) baked in an oven at a temperature of 150°C for 100 minutes; two different diameters suspended particles (polystyrene microspheres) with containing D-glucose; de-ionized water with containing D-glucose; a depolarizer; and a composite sample comprising of a depolarizer and a quarter-wave plate It is noted that the polarizers used in the tested samples for baking are polymer polarizers The baked polarizer was chosen to evaluate the performance of the proposed measurement system in measuring the optical parameters of samples with both linear birefringence and linear dichroism properties, respectively Meanwhile, two different diameters suspended particles and de-ionized water with containing D-glucose were chosen in order to evaluate the performance of the proposed method in measuring the optical parameters of turbid media with circular birefringence Moreover, the depolarizer was chosen in order to evaluate the
124 performance of the proposed measurement system in extracting the optical parameters of sample with depolarization Finally, the composite sample was chosen in order to evaluate the performance of the proposed measurement system in extracting the optical parameters of turbid media with linear birefringence and depolarization, respectively.
7.2.1 Baked polarizer as a sample (LB and LD properties)
Figure 7.9 illustrates the experimental results obtained for the LB and LD properties of the baked polarizer As expected, the measured values of the optical rotation angle, circular dichroism, and depolarization index are close to zero (see Figs 7.9(c), (d), and (e)) Due to the prolonged exposure of the polarizer to a high-temperature environment, the input light leaks through one of the dichroism axes Thus, as shown in Figure 7.9(b), the average value of the dichroism is found to be 0.974 Moreover, it can be seen that a good agreement exists between the measured values of the dichroism axis angle and the given values The average value of the phase retardance is found to be 16.91° (see Figure 7.9(a)) In addition, a good correlation is observed between the measured values of the principal axis angle and the given values From inspection, the standard deviations of the extracted values of a, B, 84 and D are found to be just 0.07°, 0.06°, 0.01° and
3.4x10°, respectively In other words, the proposed analytical model enables the parameters of hybrid samples with both LB and LD properties to be accurately determined.
Known principal axis of BP (deg.) Known principal axis of BP (deg.) Known principal axis of BP (deg.)
Known Principe ye of BP (deg.) Known principal axis of BP (deg.)
Figure 7.9 Experimental results obtained for nine effective properties of baked polarizer
7.2.2 Suspended particles with containing D-glucose (CB, L-Dep and C-Dep properties)
The performance of the proposed method in measuring the optical parameters of turbid media with CB, L-Dep and C-Dep properties was evaluated using three samples containing dissolved D-glucose powder (C6H1206, Merck Ltd.), namely an aqueous suspension of polystyrene beads with a diameter of 5 um, an aqueous suspension of polystyrene beads with a diameter of 9 um, and de-ionized (DI) water. The polystyrene bead suspensions were purchased from Thermo Scientific Ltd and had approximate concentrations of 0.32% solids (5 um beads) and 0.33% solids (9 um beads), respectively The density of both suspended particles was equal to1.05 g/cmỶ, while that of the D-glucose powder was 1.54 g/cm> The various solutions
(each with a volume of 2 mL) were contained in square glass containers with an
126 external depth of 12.5 mm and an internal depth of 10 mm In performing the experiments, the distance between the center of the sample and the detector of Stokes polarimeter was set as 23 mm in every case.
Figure 7.10 illustrates the experimental results obtained for nine effective properties of D-glucose solution with containing Sum diameter suspended particles. The average measured values of the effective parameters of the sample with different concentration of D-glucose from 0 ~ 1M (Molar) in increments of 0.1M are summarized As expected, it can be seen that a good agreement exists between the measured values of the optical rotation angle and the concentration of D-glucose over the considered range of 0 ~ 1M (see Figure 7.10(c)) From inspection, the sensitivity of the D-glucose measurement is estimated 1.72 mol/l. Moreover, the standard deviation of the optical rotation angle is found to be 0.05°. Figure 7.10(a) shows the measured value of the orientation angle of LB regarding to the concentration of D-glucose over the considered range of 0 ~ 1M A good correlation is observed between the measured values of the orientation angle of LB and the increment of the concentration of D-glucose The average value of the phase retardance is found to be 6.12° As discussed in [31-33], the analytical model yields reliable results for the orientation angle of LD are obtained only for samples with a linear dichroism greater than or equal to 0.05 Figures 7.10(b) shows that the linear dichroism of the D-glucose solution is close to zero Thus, the extracted values of the orientation angle of LD vary randomly as the concentration of D-glucose is increased As expected, Figure 7.10(d) shows that the circular dichroism of the D-glucose solution is also close to zero Figure 7.10(e) shows that good correlation is obtained between the measured values of the linear / circular depolarizations and the increment of concentration of D-glucose Moreover, the corresponding depolarization index is gradually reduced from 0.351 down 0.252 over the considered range of D-glucose (see Figure 7.10(f)).
Measured orientation angle of LD (deg.) ©8 ° a UISOJU2IP 18@UJ| painseay\| sa ˆ
Measured orientation angle of LB (deg.) g 8 ì H so} ‘ ('Bep) uoIiep1eo1 oseud paunseayy, 2is} = °a 7 a
Concentration fay ose (M) Concentration sueae (M) Concentration of D-glucose (M)
02; : có vẻ ràng Tạ eR, 4s
Measured circular dichroism ° ° fe Measured linear/circular depolarization 0 Measured depolarization index S ° 3
Concentration of D-glucose (M) Concentration of D-glucose (M) Concentration d D-glucose (M)
Figure 7.10 Experimental results for effective properties of polystyrene microspheres
Similarly, Figure 7.11 illustrates the experimental results obtained for nine effective properties of D-glucose solution with containing 9um diameter suspended particles The average measured values of the nine optical parameters of the sample with different concentration of D-glucose from 0 ~ 1M (Molar) in increments of 0.1M are summarized As shown in Figure 7.11(c), a good agreement is obtained between the measured values of optical rotation angle and the concentration of D-glucose over the considered range of 0 ~ 1M From inspection, the sensitivity of the D-glucose measurement is estimated 1.76 mol/l Moreover, the standard deviation of the optical rotation angle is found to be 0.04° Similar to Figure 7.10, Figures 7.11(a) and 7.11(b) show that both the retardance and the linear dichroism of the D-glucose solution are close to zero Thus, the extracted values of the orientation angle of LB and LD vary randomly as the increment of concentration of D-glucose Moreover, Figure 7.11(d) shows that the circular dichroism of the D-glucose solution is also close to zero Meanwhile, Figure 7.11(e) shows that the linear / circular depolarizations of 91m diameter suspended particles are close to
128 one Thus, the corresponding depolarization index is close to zero and gradually shifts from 0.041 down 0.023 regarding to the increment of the concentration of D-glucose (see Figure 7.11(f)) It is noted that the density of both suspended particles (Sum- and 9um- diameter) is 1.05g/cem3 Thus, the number of 9um-diameter particles is smaller the number of 5t1m-diameter particles in the same volume In other words, the small extracted values in depolarization index are caused by the size of diameter of suspended particles.
Concentration of D-glucose (M) Concentration of D-glucose (M) Concentration of D-glucose (M)
Concentration of D-glucose (M) Concentration of D-glucose (M) Concentration of D-glucose (M)
Figure 7.11 Experimental results for effective properties of polystyrene microspheres
As comparison of the optical rotation angles in Figs 7.10(c) and 7.11(c), Figure 7.12(a) illustrates the experimental results obtained for optical rotation angle (y) of the D-glucose solution with and without containing suspended particles It is observed that the slopes of the optical rotation angle of three different samples regarding to the concentration of the D-glucose solution are same However, the optical rotation angles of three samples have different values at 0M concentration.
As shown in Figure 7.12(b), a good agreement is observed among the optical rotation angles of three samples after calibration The process of calibration will be
—*— Polystyrene microsphere (5um) —%*— Polystyrene microsphere (5m)
S 25 —4—— Polystyrene microsphere (91m) 3 25r —â-— Polystyrene microsphere (Qum)
Concentration of D-glucose (M) Concentration of D-glucose (M)
Figure 7.12 The results of optical rotation angles of D-glucose solution with and without containing polystyrene microsphere, (a) before calibration and (b) after calibration.
7.2.2.2 Calibration in distance between sample and detector
It is noted that the distance between the sample and detector can affect the values of optical rotation angle of D-glucose with suspended particles [23] Figure 7.13 illustrates the experimental results obtained for the optical rotation angle of the suspended particle (54m and 9um diameters) solution with and without containing D-glucose regarding to various distances between the center of the sample and detector Figure 7.13(a) shows that the maximum values of optical rotation angle of the suspended particle solution without D-glucose (OM) are at 65 mm distance for Sum diameter particle case and at 15mm distance for 9um diameter particle case. Similarly, Figure 7.13(b) shows that the maximum values of optical rotation angle of the suspended particle solution with containing D-glucose (0.6M) are also at 65 mm distance for 5um diameter particle case and at 15mm distance for 9um diameter particle case.
Accordingly, the distance between the sample and detector for Sum and 94m diameter suspended particle solution is chosen as 65 mm and 15 mm respectively for the further tests Figure 7.14 illustrates that the average measured values of the
130 optical rotation angle of the sample are with different concentration of D-glucose from 0 ~ 0.6M in increments of 0.1M It is interesting that the values of the optical rotation angle at OM concentration of D-glucose on both samples are equal to zero degree Thus, the sensitivity of the D-glucose measurement is estimated 1.73 mol/l.
It is concluded that the ability of the proposed method with calibration to extract the properties of samples with circular birefringence in turbid media is first confirmed.
% Polystyrene microsphere (5um) % Polystyrene microsphere (Su)
24 181————L ©_ Polystyrene microsphere (9um) - 3 4-————— © Polystyrene microsphere (9um) , Š 8 ||
Distances from sample to detector (mm) Distances from sample to detector (mm)
Figure 7.13 The results of optical rotation angles of polystyrene microsphere (5um and
9um diameters) solutions (a) without glucose and (b) with containing glucose at 0.6 M.
—-*— 5um diameter at 65mm distance
0.8 T®—~ 9um diameter at 15mm distance
Figure 7.14 The results of optical rotation angle of D-glucose solution with containing polystyrene microsphere (Sum diameter solution at 65mm distance and 9um diameter solution at 15mm distance between sample and detector).
7.2.3 Depolarizer as a sample (L-Dep and C-Dep properties)
Figure 7.15 illustrates the experimental results obtained for the effective properties of a quartz depolarizer (DEQ-IN in ONSET Co.) Quartz depolarizer DEQ-IN converts linearly polarized input beam to unpolarized beam in a leaning of 45° against its optic axis (ONSET Co.) The average measured values of the nine effective parameters of depolarizer with different principal axis angle from 0° to 90° in increments of 15° are summarized As expected, Figure 7.15(e) shows that the linear depolarizations / circular depolarization are from 0 to 1 over the considered range of 0~90° Thus, the depolarization index of depolarizer is also changed from 0 to 1 as shown in Figure 7.15(f) It is noted that the values of depolarization index are discrete corresponding to the known azimuth angle values of depolarizer in this experiment The extracted value of the retardance varies randomly in the range of 0 ~ 180° whereas the principal axis angle of depolarizer is increased (see Figs 7.15(a)) Figure 7.15(b) shows that the linear dichroism of the depolarizer is close to zero Thus, the extracted value of the orientation angle of LD varies randomly in the range of 0 ~ 180° as the principal axis angle of depolarizer is increased As expected, Figure 7.15(c) and 7.15(d) show that both the optical rotation angle and the circular dichroism of the depolarizer are also close to zero.
† a 3 ryS 8 S ('Bep) uowepsejes oseud painseayy Measured orientation angle of LD (deg.) ©S 8 3 e FS ˆ œ °3 °Š ° i ằ ° ©œ wsio.yolp JE@UI| painseay\y, Measured optical rotation (deg.) °3 œ° °
Measured orientation angle of LB (deg.) iS
Known azimuth ng \ depolarizer (deg.) Known azimuth angie st depolarizer (deg.) Known azimuth angle of depolarizer (deg.) a Cc.
Known azimuth xi depolarizer (deg.) Known azimuth ange \ depolarizer (deg.) Known azimuth anale of depolarizer (deg.) e
Figure 7.15 Experimental results obtained for nine effective properties of depolarizer.
7.2.4 Composite sample comprising of a depolarizer and a quarter-wave plate (LB, L-Dep and C-Dep properties)
To further confirm the validity of the proposed study, a composite sample composed of a depolarizer and a quarter-wave plate is examined Table 7.1 shows the experimental results for the LB/CB, LD/CD and depolarization properties of the quarter-wave plate, the depolarizer and the composite sample with 30° and 45° principal axis angles As a result, the good agreements are observed among the measured values of nine effective parameters of the depolarizer, the quarter-wave plate and the composite sample Moreover, it is noted that the average value of retardance of the composite sample is equal to summation of the depolarizer and the quarter-wave plate in both of two considered principal axis angles Also, at 30° and 45° principal axis angle, it is observed that the linear / circular depolarization and the depolarization index of composite sample show good agreements with those of depolarizer As expected, the measured values of the optical rotation angle and the linear / circular dichroism of a quarter-wave plate, a depolarizer and a
133 composite sample are all close to zero.
Table 7.1 The experimental results of a composite sample comprising of a depolarizer and a quarter-wave plate.
Quarter-wave Quarter-wave Quarter-wave Quarter-wave Ị Depolarizer plate + Ị Depolarizer plate + at ate
Design of polarization-insensitive optical fiber probe based on effective
In practice, the optical fiber in a NSOM or interferometer system can be converted to a free-space medium by utilizing a polarization controller comprising either a variable phase retarder and a half-wave plate or two quarter-wave plates and a half-wave plate However, determining the precise settings of the various components within these controllers which guarantee the free-space condition requires a laborious trial-and-error procedure Accordingly, in the present study, a method is proposed for determining in advance the controller settings which guarantee the formation of a free-space condition In the proposed approach, the effective parameters of the optical fiber are determined using the analytical method, and the optimal settings of the various components within the two polarization controllers are then determined using a genetic algorithm The validity of the proposed approach is demonstrated by remotely and absolutely measuring the linear birefringence and linear dichroism properties of a quarter-wave plate and a polarizer, respectively.
7.3.1 Construction of free-space condition using polarization controller with variable retarder and half-wave plate
The section described in the section above was used to extract the five effective parameters of an optical fiber arranged in the four configurations shown in Table 7.2 Note that all of the experiments were performed using a single-mode optical
135 fiber (630HP, Thorlabs Co.) with a length of 47 cm The experimental setup used to characterize the optical fiber is illustrated schematically in Figure 6.1 Table 7.2 shows the extracted values of the five optical parameters of the 630HP optical fiber in each of the four considered configurations The length of all configurations is around 47 cm The way to make Configuration #1 is just to bend a single mode fiber Similarly, Configuration #2 and #3 were made by to blend reversely in the midpoint of Configuration #1 It is noted that concave of Configuration #2 is greater than concave of Configuration #3 A single loop is created in Configuration
#4 It is found that the effective retardance (B) in four configurations are 19.699, 24.02°, 25.67°, 132.07°, respectively Note that the sampling rate of polarimeter used in the experiments of measuring the output Stokes parameters is 30 samples per second Therefore, the results presented in the table indicate the mean values of the effective parameters calculated from a total of one hundred data points measurements of the output Stokes parameters All four configurations are tested and only data in Configuration # 3 is shown in this paper For Configuration #3, the standard deviation values of the orientation angle of LB (a), retardance (j), orientation angle of LD (6z), linear dichroism (D), and optical rotation (y) were as follows: 0.63°, 0.42°, 7.99°, 0.008 and 0.93°, respectively.
Table 7.2 Five effective optical parameters of 630hp optical fiber in four different configurations.
7.3.1.1 Principle of free-space media construction using variable retarder and half-wave plate
As discussed in Section 6.3, it is desirable to convert the optical fiber in a NSOM or interferometer system into a free-space medium such that the system can be illuminated using any form of polarization light Table 7.2 shows that the linear dichroism of the 630HP optical fiber is close to 0 In other words, in constructing the free-space medium, the linear dichroism property of the fiber can be ignored. That is, the fiber can be characterized in terms of its LB and CB properties only. Figure 7.16 presents a schematic illustration of a typical polarization controller used to render an optical fiber insensitive to the polarization state of the input light.
As shown, a variable retarder (VR) and half-wave plate (HP) are inserted between the power meter and the fiber coupler used to couple the input polarization light into the optical fiber The VR compensates for the LB property of the fiber, while the HP compensates for the CB property Thus, through an appropriate setting of the orientation angle and retardance of the VR, and the optical rotation of the HP, the optical fiber can be converted into a free-space medium with negligible linear or circular birefringence.
RHC or Free- space unit
LP LHC LP matrix media
) Variable Half-wave | retarder plate
He-Ne Laser h ' mà | Fiber |
Q45°,-45° p Neutral Power | Fiber-coupler. density meter |
Figure 7.16 Schematic illustration of common-path interferometer with polarization-insensitive fiber probe.
7.3.1.2 Experimental verification of GA optimization procedure
The validity of the GA optimization procedure was evaluated experimentally for the polarization controller shown in Figure 7.16 using an LVR-100 (Meadowlark Optics Co.) variable retarder and an 04PLM-3M (CVI) half-wave plate In performing the experiments, the polarizer P (GTH5M, Thorlabs Co.) and the quarter-wave plate Q (QWP0-633-04-4-R10, CVI Co.) were used to produce linearly polarized lights orientated at 0°, 15°, 30°,45°,60°, 75°, 90°, 105°, 120°, 135°, 150°, 165° and 180° to the horizontal plane, right- and left-hand circular polarization lights, and elliptical polarization lights Furthermore, the polarization lights were passed through the neutral density filter and power meter detector in order to ensure that each light had an identical intensity when entering the VF/HP/fiber structure It is noted that the sensor of power meter detector will be taken out from the measurement system after the intensity of the polarization light is identified During the experimental process, the input voltage of the VR was maintained at a constant value, yielding a constant retardance, By The principal axes of the VR and HP (avy and yu) were then gradually rotated until a free-space unit matrix condition was achieved (i.e the output polarization states were identical
138 to the input polarization states).
Table 7.3 compares the values of ay, By and yHobtained from the GA with the corresponding experimental values for the four optical fiber configurations shown in Table 7.2 It is observed that a good agreement exists between the two sets of results in every case As a result, the basic validity of the GA optimization procedure is confirmed.
Table 7.3 Comparison of GA results and experimental results for values of ay,
By and yu required to obtain free-space condition in Figure 7.16.
GA Experiment Configuration No./ Fiber effective parameters Half-wave plate + Half-wave plate +
Taking the HP/VR settings for Configuration #3 in Table 7.3 for illustration
139 purposes, a series of experiments was performed in order to compare the azimuth angles () and ellipticity angles (x) of the input and output polarization lights The corresponding results are shown graphically in Figure 7.17 In Figure 7.17, it is seen that the azimuth angle of the output light is linearly correlated with the azimuth angle of the input light for all linear polarization states Furthermore, the ellipticity angle of the output light is equal to approximately zero for all angles of the linear polarized light It is noted that this discrepancy can be attributed to various errors within the measurement system, such as variations and mis-alignments in optical components or non-identical intensities in calibration. The influence of environmental conditions (such as temperature) to the experimental results also could be a factor Overall, the results presented in Figure 7.17 confirm that the azimuth and ellipticity angles of the light emerging from the VR/HP/fiber structure are virtually identical to those of the light entering the VR.
In other words, a free-space condition is successfully achieved when using the optimal VR and HP settings determined by the GA.
Figure 7.17 Comparison of azimuth angles and ellipticity angles of input / output lights given input lights with different linear polarization states.
Having confirmed the feasibility of the GA algorithm for optimizing the settings
140 of the VR and HP in Figure 7.16 for linear input polarization lights, a further series of experiments was performed to evaluate its feasibility given right-hand and left-hand circular input polarization lights, respectively The results presented in Table 7.4 confirm that a good agreement exists between the ellipticity angles of the input and output lights in both polarization states In other words, the results confirm the ability of the GA to determine the experimental settings of the VR and
HP which result in a free-space condition when the optical fiber is illuminated with circular polarization light.
Table 7.4 Comparison of ellipticity angles of input/output lights given input lights with right- and left-hand circular polarization states.
Circular polarization Right-hand | Left-hand
Figure 7.18 compares the azimuth/ellipticity angles of the input/output lights in the free-space unit matrix media given input lights with various randomly-selected right- and left-hand elliptical polarization states, respectively It can be seen that in every case, the azimuth angles and ellipticity angles of the output light are in good agreement with the equivalent angles of the input light In other words, the ability of the GA to predict the VR and HP settings which result in a free-space condition given a random elliptical polarization state of the input light is confirmed.
Figure 7.18 Comparison of azimuth angles and ellipticity angles of input / output lights given input lights with randomly-chosen right- and left-hand elliptical polarization states.
Overall, the results presented in Table 7.4 and Figs 7.17 and 7.18 confirm that the GA optimization procedure provides the means to obtain the values of av, v and yu which result in a free-space condition when using the polarization controller shown in Figure 7.16 with linear, circular or elliptical input polarization light. (Note that while the discussions above have considered only Configuration #3 of the optical fiber, similar findings were obtained for Configurations #1, #2 and #4.)
7.3.2 Construction of free-space condition using polarization controller with two quarter-wave plates and one half-wave plate
The feasibility of the GA optimization procedure was evaluated for an alternative polarization controller comprising a half-wave plate sandwiched between two quarter-wave plates Since the 630HP fiber has negligible LD properties (see Table 7.2), the effect of the QW2/HP/QW /fiber arrangement on the input polarization light can be described using the following unit matrix.
LM owi ILM pe IM ¿y; = [M rived (7.3.1) where [Mowi] and [Mow¡] are the Mueller matrices of QW: and QW2, with two variable parameters (i.e ®ọi and ®q2) and [Mup] is the Mueller matrix of the HP with one variable parameter (i.e Dy).
The GA optimization procedure was used to determine the values of Dai, Daz and ®y required to obtain a free-space condition for linear polarization input light and the four fiber configurations shown in Table 7.2 Given effective fiber parameters of a = 114.81°, B = 25.67° and y = -23.55°, (i.e Configuration #3, see Table 7.2), the corresponding settings of the polarization controller were found to be as follows: ®ọi = 46.06°, ®n= 64.28° and ®ọ;= 69.65° Utilizing Configuration