MEASUREMENT OF LINEAR AND CIRCULAR DIATTENUATION
IN OPTICAL ELEMENTS
Technical Field
[0001] This application relates to precise measurement of linear and circular diattenuation in optical elements.
Background and Summary
[0002] Many optical elements display a property known as diattenuation, whereby the intensity transmittance of a beam that exits an optical element or sample is a function of the polarization state of the incident beam. The intensity transmittance is a maximum Tmax for one polarization state of the incident beam, and a minimum Tm1n for the orthogonal polarization state for that beam.
[0003] Linear diattenuation needs two parameters to describe it: (1) angle θ which is the angle of the maximum transmission axis for linearly polarized light; and (2) magnitude Ld, which is defined as (Tmax - Tmin)/( Tmax + T1111n).
[0004] What follows is a description of a system for measuring, in addition to linear birefringence of an optical element, the linear and circular diattenuation properties of that element.
Brief Description of Drawings
[0005] Fig. 1 is a diagram of one embodiment of the instrumentation used with the present invention, including a light source module, an optical element or sample, and a detector module.
[0006] Fig. 2 is a block diagram of a preferred version of a light source module.
[0007] Fig. 3 is a diagram for illustrating motion controllers used with the instrument.
[0008] Fig. 4 is a diagram showing the use of visible laser light as a guide for the actual beam used in the measurement calculations.
[0009] Fig. 5 is diagram illustrating a variable aperture for use in a detector module in instances where the source light beam collimation is modified by the sample.
[0010] Fig. 6 is a diagram showing the use of a re-collimating lens and fixed aperture for use in a detector module in instances where the light beam collimation is modified by the sample.
Description of Preferred Embodiments
[0011] One preferred embodiment of the present invention includes (see Figs. 1 and 2) a light source module 20 that contains a deuterium lamp 22 (30 W), a wavelength selecting device 24
(narrow band filter) and light collimating lenses 26.
[0012] Polarizers, such as Rochon polarizers are located in the source module 20 and detector module 40 as shown. The source module polarizer 28 is oriented at 45 degrees, and the detector module polarizer 30 is oriented at 0 degrees.
[0013] A photoelastic modulator (PEM) 32 is located in the source module with its optic axis at 0 degrees. The PEM 32 modulates the polarization of the source light beam "B." A second
PEM 34 is in the path of the beam "B" and is oriented at 45 degrees. The optical element of interest (hereafter sample 36) is located between the source and detector modules, hence between the two PEMs 32, 34. The two PEMs have different frequencies (for example, 50
KHz and 60 KHz, respectively).
[0014] The detector 42 may be a photomultiplier tube (PMT).
[0015] The instrument illustrated in Fig. 1 is essentially a polarimeter specifically designed for determining linear retardation (both magnitude and angle of fast axis) linear diattenuation
(both magnitude and angle of maximum transmission axis) circular retardation and circular diattenuation in a sample. To measure both the birefringence and diattenuation of a sample, only one optical configuration, as shown in Fig. 1, is required. There is no need to rotate the source and detector modules or associated optical components.
[0016] The results of theoretical analysis using Mueller matrices for the dual PEM-single detector configuration shown in Fig. 1 are provided next.
The variables δl and δ2 are the time varying phase retardation of the respective PEMs 32, 34
(δl = δlosincϋit and δ2 = δ20sincϋ2t); and cϋi and ω2 are the PEM modulating frequencies of the respective PEMs 32, 34; and δl0 and δ20 being the peak retardation amplitudes of the respective PEMs 32, 34.
[0017] If the sample exhibits both linear retardation and linear diattenuation, the corresponding DC signal at the detector 42, while δlo = δ2o = 2.405 radians (0.3828 waves), is:
KT VDC = -^- Eqn. (1).
[0018] The useful AC terms for determining linear retardation (both magnitude and angle) and linear diattenuation (both magnitude and angle) in a sample can be obtained using the Bessel function expansions:
sin Sl = sin(δl0 sin(<sy)) = ∑ 2 J2k+l (Sl0 ) sin((2£ + l)ωxt) Eqn. (2)
2k+l cos Sl =
= J
0 (Sl
0 ) + ∑ 2J
2lc (Sl
0 ) cos((2k)ω
xt) Eqn. (3)
2k and similar expansions of sinδ2 and cosδ2, where k is either "0" or a positive integer that represent the order of the Bessel function.
[0019] For measuring linear birefringence below a quarter of the wavelength of the light source, the useful terms are the (2(D1 + ω2) and ((D1 + 2ω2) terms:
KI V 2o^oh = ~γ 2Mδlo) - 2Ji (S20) cos(2p) sin S Eqn. (4.1)
KI1
V2oh + Oh = ^2J2(Sl0) . 2J1(Sl0) Un(Ip) Un S Eqn. (4.2)
[0020] In order to eliminate the effect of light intensity variations due to light source fluctuations and the absorption, reflection and scattering from the sample and other optical components, the ratios of the AC signals to the DC signal are used. The ratios of AC signals to the DC signal for the (2(D1 + ω2) and ((D1 + 2ω2) terms are represented in equations (5.1) and (5.2):
V1 L C,O1 + U)2
= 2J2 (Sl0) - 2J1 (S20) cos(2p) sin S Eqn. (5.1) * DC
K 2a>2 + o\ = 2J1 (S20) • 2J1 (Sl0) sin(2yø) sin S Eqn. (5.2)
DC
[0021] Defining R1 and R2 as corrected ratios, equations (5.1) and (5.2) become:
K 2o\ + (O2 = R1 = cos(2/}) sin S
VDC 2J2(Sl0) - 2J1(Sl0) Eqn. (6.1)
V 2ι»2 + °\ = R2 = sin(2/}) sin S
VDC 2 J2 (S20) - 2 J1 (Sl0) Eqn. (6.2)
[0022] Rearranging equations (6.1) and (6.2), we can express the retardation magnitude and angle of fast axis of the sample as:
[0023] where δ, represented in radians, is a scalar. When measured at a specific wavelength (i.e. 193 nm), it can be converted to retardation in "nm" (δnm = δrad-193/(2π)).
[0024] For measuring linear diattenuation, the useful terms are the 2ωl and 2ω2 terms:
KL
K 2^ωλ = 2J2(Sl0) - Ld - sin(2<9) Eqn. (8.1)
KL
* 2 ω, ~~ 2 J22 V(S—l 00)/ • L ^d" • c —os( V2—6>) J Eqn. (8.2)
[0025] where θ is the angle of the maximum transmission axis for linearly polarized light, Ld is defined as (Tmaχ - Tmin)/( Tmax + Tm1n), where Tmax and Tmin are the maximum and minimum intensities of transmission for linearly polarized light.
[0026] The ratios of the AC signals to the DC signal are:
V 2ωx
= 2 J2 (Sl0) - Ld - sin(20)
V Eqn. (9.1)
D1 C
V 2 «2 = 2JJSl0) - Ld - cos(2<9)
V1 Eqn. (9.2)
DC
[0027] Defining LR1 and LR2 as corrected ratios for linear diattenuation, we have:
V 2 ωx
= LR1 = Ld - sin(26>)
VDC - 2J2 (Sl0 ) Eqn. (10.1)
V 2 ω2 = LR2 = Ld • cos(2<9)
VDC . 2J2(S20) Eqn. (10.2)
[0028] Rearranging equations (10.1) and (10.2), we can express the retardation magnitude and angle of fast axis of the sample as:
Eqn. (11.2) [0029] For measuring circular diattenuation, the useful terms are the GO1 and ω2 terms:
2J
1(Sl
0) - Cd Eqn. (12.2)
[0030] where the circular diattenuation (Cd) is defined as (TR
CP - TL
CP)/( TR
CP + TL
CP), where
TRCP and TLCP are the intensities of transmission for right and left circularly polarized light, respectively.
[0031] The ratios of the AC signals to the DC signal are:
= 2J
1 (Sl
0) - Cd Eqn. (13.1)
' DC
V O) 2 = 2J1(SIz) - Cd Eqn. (13.2)
V r DDCC or
V
[0032] This instrument also provides the measurements of circular brief (optical rotation). Turning to a preferred implementation of the present invention, wavelength selection can be performed using a narrow band optical filter 24 (Fig. 2) (e.g. 193 nm) instead of a monochromator. This minimizes the size and weight of the source module 20 and optimize light delivery but possibly limit the wavelength resolution. Alternatively, one may use a simplified monochromator (grating at a fixed position) for selecting 193 nm light only. [0033] The system of the present invention also includes semi-automated system with software MACROs to reduce motion complexity. Five motion controls are employed (Fig. 3). The source module includes a linear translation stage 52 and a tilt stage 54. The sample 36 (in this instance, a lens of varying power and thickness) includes a rotation stage 56. The detector module includes a linear translation stage 58 and a tilt stage 60. Accordingly, the system includes five motion controllers. [0034] The operation of the system (reference Fig. 3) includes the steps of
• manually generate measurement coordinates of the five motion controls for the first sample 36;
• manually align source module 20 to the sample (eg, a lens) by adjusting linear motion control 52 and tilting motion control 54;
• manually align detector module 40 to receive optimized light intensity by adjusting linear motion control 58 and tilting motion control 60;
• Due to the symmetry of the lens sample, once the coordinates of linear motion control 52, tilting control 54, linear motion control 58 and tilting control 60 are chosen, all coordinates of the remaining (sample) rotational control 56 can be generated by rotating the lens sample one full turn; (Alternatively, the sample could be held stationary and the modules 20, 40 rotated instead.)
• Create software instructions (MACRO) based on the manually generated coordinates
• Use MACRO for automation in subsequent measurements of the same type of lenses. [0035] The aligning steps noted above can be assisted by using two or more visible lasers as guides as shown at "VL" in Fig. 4. The lines inside of the visible laser light "VL" enclose the source light beam, which may have a wavelength of 193 nanometers, and is difficult to observe with the naked eye.
[0036] Finer motion control, if needed, can be included on one of the modules to get optimal light intensity delivery.
[0037] The advantages of using PEMs for lens measurement system include a large useful aperture and acceptance angle.
[0038] As respects the treatment of a non-collimated beam exiting the (lens) sample 36 one could use aperture diameter control 62 (represented by the opposed arrows in Fig. 5), which, like the motion controllers discussed above, may be computer controlled. The diameter of the aperture is related to the amount of convergence or divergence of the light beam introduced by the sample 36, which, as noted can be a lens of varying optical power.
[0039] Alternatively, one could use a re-collimating lens 64 and a fixed aperture 66 in front of active area of the detector (see Fig. 6). The focused or diverged beam B emanating from the sample lens under measurement is directed to that re-collimating lens 64 before passing through the fixed aperture 66.
[0040] While the present invention has been described in terms of preferred embodiments, it will be appreciated by one of ordinary skill in the art that modifications may be made without departing from the teachings and spirit of the foregoing.