JP4657105B2 - Measurement of out-of-plane birefringence - Google Patents

Description

  The present invention relates to the measurement of birefringence properties of optical materials, and basically relates to the measurement of out-of-plane birefringence of such materials.

  Many important optical materials exhibit birefringence. Birefringence causes different linear polarizations that pass through the material at different speeds. These different polarizations are considered to be two components of polarized light where one component is orthogonal to the other.

  Birefringence is an inherent property of many optical materials and can be introduced by applying an external force to the material. The birefringence introduced in this way occurs temporarily as when the birefringence oscillates, or often occurs, for example, when the material is subjected to thermal stress during the manufacturing process of the material, The birefringence may remain.

  Delay, or retardance, represents the integrated result of birefringence acting along the path of rays through a sample of optical material. When the incident light beam receives linearly polarized light, two orthogonal components of the linearly polarized light are present in the sample with a phase difference called retardance. The basic unit of retardance is a nanometer (nm) length. However, it is convenient to express it in units of phase angle (wavelength, radians or degrees) proportional to the retardance (nm) divided by the light wavelength (nm). The “average” birefringence for a sample may be calculated by dividing the measured retardance magnitude by the thickness of the sample.

  The two orthogonal polarization components described above are parallel to the two perpendicular axes for the optical material or sample, both perpendicular axes being referred to as the “fast axis” and the “slow axis”. The fast axis is the axis of the sample that is aligned with the fast polarization component passing through the sample. Therefore, a complete description of a sample's retardance along a given optical path should specify both the magnitude of the retardance and the relative angular orientation of the fast axis (or slow axis) of the sample. I need.

  The need to accurately measure birefringence characteristics is becoming increasingly important in many technical applications. For example, it is important to identify the linear birefringence of optical elements used in high precision instruments employed in semiconductors or other industries.

  Prior art, including US Pat. No. 6,473,747, “birefringence measurement apparatus” incorporated herein by reference, uses a light beam directed at the sample at a normal (zero angle) angle of incidence with respect to the sample surface. A birefringence measuring method and apparatus are disclosed. As a result, the determination of the birefringence of the sample is “in-plane”, which basically determines the refraction of two orthogonal axes in the plane perpendicular to the incident light of the sample. It means to show the difference in rate.

  The effect of birefringence in visible light that is displayed (such an effect occurs when, for example, light passes through an optical film or coating) will reduce contrast or change color. Also, in many materials such as those used in liquid crystal display (LCD) panels, the degree or magnitude of birefringence is considered to be a function of the incident angle of the light beam. For example, increasing the viewing angle (from the normal) when looking at an LCD panel increases the birefringence effect of rays emanating from the panel, and without correction, reduces the perceptual quality of visible light by reducing contrast and / or color changes I will let you.

  Transparent polymer films have been developed for use in LCD panels to compensate for the now famous birefringence caused by viewing angle changes. In summary, these films have birefringent properties that compensate for the birefringence of the LCD panel, thus providing a wide viewing angle without incurring significant loss of contrast or color.

  It is important to properly characterize birefringence in planes parallel to the normal (zero angle) angle of incidence of such films and other optical materials. This measurement of birefringence can be referred to as “vertical” or “out-of-plane” birefringence. The concept of in-plane and out-of-plane refraction can be considered in terms of an orthogonal coordinate system. Therefore, assuming that normal incident light travels in a direction parallel to the Z-axis of such a coordinate system, the in-plane birefringence occurs on the XY plane of the sample. Out-of-plane birefringence is in a plane perpendicular to the in-plane birefringence and thus occurs in the XZ or YZ plane.

  Other applications (in addition to the birefringence compensation film example just mentioned) require an accurate determination of out-of-plane birefringence. For example, certain isotropic crystals, such as calcium fluoride, exhibit intrinsic birefringence when short wavelength light (eg, 157 nm) propagates through the crystal. Its intrinsic birefringence is maximized in a plane parallel to the [110] axis of the crystal. Such crystals also have an outer surface or “window” for receiving incident light perpendicular to the [111] plane of the crystal perpendicularly. As a result, the intrinsic birefringence appearing on the [110] axis of the crystal just described becomes out-of-plane birefringence with respect to light perpendicular to the [110] plane, and thus follows the measurement technique of the present invention as summarized below.

  The present invention is directed to precise measurement of out-of-plane birefringence of a sample made of a transparent optical material.

  In one preferred embodiment, two angularly separated beams are passed through a selected location on the sample. One of the two rays is directed at an angle of incidence perpendicular to the sample surface. The characteristics of both rays are detected after passing through the sample, and the information obtained is processed to determine out-of-plane birefringence.

  Other advantages and features of the invention will become apparent upon review of the following description and drawings of the specification.

  According to the present invention, the out-of-plane birefringence that occurs at a location on the sample is determined by passing two angularly separated rays through the location. One of both rays is directed perpendicular to the surface of the sample. Thus, when the one light beam exits the sample, it provides information regarding the in-plane birefringence of the sample.

  The other ray is directed obliquely to the sample surface, thus with characteristics that provide information relating to the retardance that occurs along the (refracting) incident path of the second ray through the sample. Exit from the sample. Information provided by two angularly separated rays is detected and described in more detail below to provide out-of-plane birefringence of the sample in addition to in-plane birefringence of the sample. Receive a process like this.

  One embodiment of an apparatus for measuring out-of-plane birefringence is described with reference to FIGS. The schematic diagram of FIG. 1 shows the main optical elements of the device. The optical elements are grouped and described as modules. The embodiment of FIG. 1 describes a vertical source module 10, a vertical detection module 12, an oblique source module 14, and an oblique detection module 16. The terms “vertical” and “oblique” are used herein to refer to modules associated with rays directed at the sample at a right angle, ie, an incident angle of zero, respectively, and to the sample at an oblique angle, as detailed below. It is used as an adjective to distinguish the module associated with the light beam being directed.

  The components of the vertical source module 10 include a He—Ne laser as the light source 20. The laser has a wavelength of 632.8 nanometers (nm). The wavelength of the light source can be selected to best suit a particular application.

  The light beam “B” emitted from the light source 20 has a cross-sectional area or “spot size” of about 1.0 millimeter (mm). The light source beam is directed to enter a polarizer 22 that is directed in a +45 degree polarization direction with respect to a reference axis. A polarizer exhibiting high quenching properties such as Gran-Thomson calcite is preferred. Further, it is preferable to attach the polarizer 22 to a rotating body that operates in an elaborate and stepwise manner.

  Polarized light emitted from the polarizer 22 is incident on the optical element 24 of the photoelastic modulator 25. In a preferred embodiment, the photoelastic modulator (hereinafter referred to as “PEM”) is a PEM manufactured by Hinds Instruments, Inc., located in Hillsboro, Oregon. Although PEM is preferred, it should be noted that other mechanisms can be used to modulate the polarization of the source beam.

  The most accurate retardance measurement is achieved when the residual birefringence that appears in the optical elements of the device is minimized. For this purpose, the PEM 25 should be configured to eliminate residual birefringence that may be caused by the support effects of the optical elements 24 of the PEM.

  The PEM 25 has a birefringence axis oriented at 0 degrees and is controlled by a controller 84 that imparts vibrational birefringence to the optical element 24, preferably at a nominal frequency of 50 kHz. In this regard, the controller drives two quartz transducers with an optical element 24 bonded between the quartz transducers.

  The vibrational birefringence of the PEM 25 causes a time-varying phase difference between orthogonal components of polarized light propagating through the PEM. At any instant, the phase difference is a retardation caused by the PEM. As mentioned earlier, the delay can be measured in units of length such as nanometers. The PEM is adjustable so that the magnitude of the delay caused by the PEM can be changed. At hand, the magnitude of the delay is selected to be 0.383 wavelength (242.4 nm).

  The light beam “B1” propagating from the PEM 25 is directed through the transparent sample. The sample is supported in the path of the light beam (here, in the Z-axis direction) by a sample holder 28 that can be controlled to periodically move the sample in a translational sense along an orthogonal (XY) axis. Think of the rays going to).

  Since the sample 26 may be, for example, a thin and flexible polymer film, the holder may be a plurality of spaced apart, small diameter (eg, 1 or 2 millimeters) wires tightly stretched between two rigid support members. The thing containing is preferable. For the wire, a wire rope made of stainless steel coated or not coated with a low friction coating can be used. Also, wire ropes coated with nylon and many other materials can be used as the wire. The wire, the tension of the wire, and the spacing between the wires are selected according to the weight of the sample so that the sample is supported on a plane that does not exert bending stress that causes slack in the sample. . The spacing between the individual wires of the holder 28 is as large as possible (depending on their own weight and the flexibility of the sample 26), and as described above, the space occupied by the wires lying below the wires is minimal. It becomes.

  As described above, the sample holder 28 can be driven by the conventional XY stage mechanism for translating the sample, and thereby, a plurality of positions in the entire region of the sample 26 are reflected by the light beam “B1”. Can be scanned.

  When the light beam “B1” passes through the sample 26, it is affected by the in-plane birefringence of the sample. As described above, the light beam is delayed due to the influence. The in-plane birefringence that causes this delay is determined in accordance with the present invention and is used to determine out-of-plane birefringence, as described below.

  For a clear measurement of the in-plane delay introduced into the sample, the beam “B1” passing through the sample 26 is separated into two parts having different polarization directions, for which two information A channel is defined.

  A suitable mechanism for separating the light beam “B1” includes a beam splitting mirror 30 that is a component of the vertical detection module 12 and is disposed in the light beam path (hereinafter referred to as an incident path). The beam splitting mirror 30 is preferably made of a Schott Glass type SF-57. This glass has a stress optical coefficient that is extremely low (close to 0). Although a beam splitting mirror is preferred, other mechanisms (such as flipper mirror arrangements) to separate the beam “B1” into two parts can be used instead.

  When the beam or beam “B1” has completely passed through the beam splitting mirror 30, it enters a detection device 32 for detection, as represented by “B1l”. The detection device 32 includes a small Glan-Taylor type analyzer 42 arranged in a polarization direction of −45 degrees from the reference line. From the analyzer 42, the light beam “B1l” enters a detector 44 which will be described further below.

  The reflecting surface of the beam splitting mirror 30 is upward and faces the sample 26. The mirror is installed so that the incident path (that is, the optical path of the light beam “B1” propagating from the sample 26) is substantially perpendicular to the reflecting surface of the mirror. In a preferred embodiment, the angle between the light beam “B1” traveling along the incident path and the partial light beam “B1R” reflected by the mirror 30 is greater than 0 degrees and less than 10 degrees.

  The reflected partial beam “B1R” is incident on the other detection device 50. The detection device 50 is configured and arranged to be close to the incident light beam “B1” and is positioned to receive the reflected light beam “B1R”. The components of the detection device 50 are integrally miniaturized and housed to include a Gran-Taylor analyzer 74 arranged so that the polarization direction is 0 degrees parallel to the birefringence axis of the PEM 25. .

  On the analyzer 74, a narrowband interference filter 77 is stacked that allows passage of polarized laser light but prevents unwanted room light from reaching the detector 76. The detector is preferably a photodiode stacked on the filter. The photodiode detector 76 is a suitable detection mechanism, and outputs a current signal representing the time-varying intensity of the received laser light. Regarding the detection device 50, the detected laser beam is a laser beam of the light beam “B1R”, and is a portion where the light beam propagated from the sample 26 is reflected.

  The photodiode output of the detection device 50 is transmitted to a preamplifier held on an associated printed circuit board (not shown) that is part of the detection device 50. The preamplifier is output to a phase sensing device (preferably a digital signal processing element using a lock-in amplifier 80 or an equivalent computer) in the form of a low impedance intensity signal VAC1R and a DC intensity signal VDC1R indicating a time average of the sensor signal. 75 (FIG. 2) is supplied.

  The detection device 32 that is the other detection device 32 (FIG. 1) and to which the non-reflective portion “B1l” of the light beam “B1” is directed is the same as the detection device 50 described above except for two points. It is a simple configuration. In the detection device 32, the polarization direction of the analyzer 42 is oblique to the polarization direction of the analyzer 74 of the other detection device 50. In particular, the analyzer 42 is arranged with a polarization direction of −45 degrees. The photodiode of the detection device 32 is a non-reflective portion “B1l” of the light beam “B1” that outputs a current signal indicating the time-varying intensity of the received laser light and propagates through the sample 26.

  The output of the photodiode of the detection device 32 is transmitted to a preamplifier, which pre-amplifies the output 79 in the form of a low impedance intensity signal VAC1 and a DC intensity signal VDC1 indicating the time average of the sensor signal. ) Is supplied with output 75 (FIG. 2).

  In summary, the lock-in amplifier 80 has two input channels. One corresponds to the output of the detection device 32, and the other channel corresponds to the output of the detection device 50. The intensity information obtained by the lock-in amplifier via the first channel is related to the 0 degree or 90 degree delay characteristic (retardance) component introduced into the sample 26 due to the arrangement of the −45 degree analyzer 42. . The intensity information received by the second channel of the lock-in amplifier 80 is related to the 45 degree or -45 degree delay component introduced into the sample as a result of the placement of the 0 degree analyzer 74. As will be explained below, this information is the total amount of information provided to the beam “B1” (ie, the normal incident beam) at the scan position of the sample, as well as the direction of the fast axis at that location of the sample. Combined with an algorithm that produces a result that unambiguously determines the magnitude of the delay.

  The lock-in amplifier 80 receives the oscillation frequency supplied by the PEM controller 84 that drives the optical element 24 of the PEM 25 as the reference signal 82. A lock-in amplifier 80 is connected to this to provide the digital computer 90 with the value at that position of the sample received on two channels which can be designated as channel 1 and channel 2 described above. . The intensity signals of channels 1 and 2 of both detectors are derived as follows:

Where Δ is the time-varying phase delay of the PEM, δ _N is the magnitude of the delay with respect to the sample beam “B1”, and ρ is the fast axis azimuth of the sample delay. The Mueller matrix for the linear birefringent sample (δ, ρ) used for the derivation has the following general formula.

In equation (1), sin Δ (Δ = Δ ₀ sin ωt, where ω is the modulation frequency of the PEM and Δ ₀ is the maximum peak delay of the PEM) can be expanded by the first type Bessel function.

Here, k is “0” or a positive integer, and J _{2k + 1} is a (2k + 1) -th order Bessel function. Similarly, cosΔ can be expanded by a Bessel function of even harmonics.

Here, J ₀ is a 0th order Bessel function, and J _2k is a (2k) th order Bessel function.

  As can be seen from the equations (1) to (3), it is preferable to determine the delay characteristic, that is, the magnitude of the retardance and its azimuth using the signal at the first harmonic of the PEM.

Useful signal for measuring the linear birefringence in the second harmonic of PEM, compared to sin [delta _N is corrected by sin ² (δ _N / ²⁾ is extremely small value. The 1F electronic signal shown by the detector can be expressed by equation (4).

  As described above, the 1F signal is determined using the lock-in amplifier 80 referred to by the first harmonic of the PEM. The lock-in amplifier eliminates contributions from all harmonics except 1F. The outputs for the two channels from the lock-in amplifier 80 are as follows:

Because of the low level linear birefringence, an approximation of sin δ _N ≈δ _N is used and the fact that the lock-in amplifier measures the mean square of the signal results in √2 rather than amplitude.

All terms appearing at frequencies other than the first harmonic of the PEM are ignored by obtaining equation (5). The validity of the equation (5) for obtaining the 1F VAC signal is guaranteed by the approximation result that sin ² (δ _N / 2) ≈0 when δ _N is small. This is suitable for a low level delay characteristic (retardance) of, for example, 20 nm or less.

The ratio of the 1F VAC signal to the VDC signal is used to remove the effects of fluctuations in the intensity of the light source or the effects of changes in transmission due to absorption, reflection loss or scattering. (Alternatively, a similar method can be used to dynamically and uniformly normalize the DC signal.) Eliminating the cosΔ term in equation (1) is a high quality lock-in amplifier. It has a minimal impact on making 1F VAC signal decisions, but has a significant impact on the channel 1 VDC signal. The term cos ² (δ _N / 2) cos Δ in equation (1) approximates the value of cos Δ when δ _N is small. As can be seen from equation (3), the value of cosΔ depends on J ₀ (Δ ₀ ) and is a term of “DC”. As a result, this DC term can be corrected as shown in Equation 7.

Here, R _ch1 and R _ch2 are amounts determined from two channels, respectively.

The PEM delay is set so that J ₀ (Δ ₀ ) = 0 (when Δ ₀ is 2.405 radians or 0.383 wavelength) for correction of the “DC” term caused by the cos Δ term in channel 1. With this PEM setting, the PEM efficiency for generating the 1F signal is about 90% of its maximum.

Finally, the measured amount δ _N (nanometer) of the in-plane delay affecting the normal incident light beam “B1” and the angular direction ρ are expressed by Expression (8).

  These equations (8) are compiled into a program that runs on the computer 90, and such delay characteristics (retardance) at selected locations in the sample through which the angularly separated rays propagate. Used to determine size and azimuth.

Equation (8) was developed especially for small linear birefringence. The approximation of sin δ _N ≈δ _N used to derive equation (8) has an error of about 1% for δ = 20 nm when the wavelength of light is 632.8 nm. For large delay characteristic (retardance), sin [delta _N is used instead of the [delta] _N.

  Despite the above-described attempts to remove residual birefringence in components of devices such as the PEM, the presence of at least some residual birefringence is unavoidable. In the device of the present invention, a highly accurate result is obtained by correcting the result of equation (8) to nullify any residual residual birefringence referred to as the device's offset. Actually, the residual birefringence in the optical element of the photoelastic modulator and the beam splitting mirror substrate may cause an error in the measurement result. Such errors can be measured by first operating the device in the absence of a sample. Error correction is performed by subtracting the error value of each channel. In principle, the procedure provides a self-calibration method for the device. However, it is advisable to compare sample measurements with this device to measurements obtained using other methods.

The value of the delay characteristic (retardance) δ _N introduced by the in-plane birefringence of the sample is the same as the measurement of the delay characteristic (retardance) given to the other light beam shown as “B2” in FIG. Used. As described above, the light beam “B2” is directed obliquely toward the surface of the sample 26. As such, ray “B2” exits the sample with features that provide information related to the delay characteristics (retardance) that occur along the (refractive) incidence path of ray “B2” passing through the sample. Thus, the information provided by the two angularly separated rays “B1” and “B2” is detected to provide out-of-plane birefringence of the sample in addition to in-plane birefringence of the sample. And processed as well.

  Except as noted below, the diagonal source module 14 and the diagonal detection module 16 are comparable to the vertical source module 10 and the vertical detection module 12, respectively. Accordingly, the oblique source module 14 includes a light source 220, a polarizer 222, and a PEM 225 that function similarly to the light source 20, the polarizer 22, and the PEM 25 of the vertical source module 10. Similarly, the oblique detection module 16 includes a beam splitting mirror 230 and detection devices 232 and 250 that function similarly to the beam splitting mirror 30 and detection devices 32 and 50 of the vertical detection module 12. In the oblique detection module 16, the light beam “B2” is thus divided into two parts “B2I” and “B2R” and subjected to the same processing as the light beam parts “B1I” and “B1R” in the vertical detection module 12.

  The fundamental difference between the vertical modules 10, 12 and the diagonal modules 14, 16 is that they pass through the sample 26 at an angle “A” in FIG. 1 that is oblique with respect to the normal incident beam “B1”. It is used to provide and detect the propagating ray “B2”. For this purpose, in this embodiment, the oblique source module 14 is mounted away from the vertical source module 10 and also angularly separated rays “B1” and “B2” that propagate through the same position in the sample. It is tilted to produce "".

  In one example, the angle “A” is selected to be 30 degrees. Since the calculation of out-of-plane birefringence described later includes information derived from both rays “B1” and “B2”, the angle “A” is perpendicular to the position where the oblique angle ray “B2” enters the sample. A small angle is preferred to ensure that it is substantially aligned with the position where the beam “B1” enters and that the dimensions at both positions are not significantly different. In consideration of these matters, treatment is performed to deflect both rays by 30 degrees.

Those skilled in the art will apply the lock-in amplifier 280 (see FIG. 2) to be processed by the computer 90 following the above discussion regarding the vertical detection module 12 and the associated processing of the light beam “B1” received by the detection module. It will be appreciated that the detected signal produces a delay characteristic (retardance) measurement δ _N (nanometers) in the oblique ray “B2”. This information is obtained from the measured vertical delay δ _N for the preferably simultaneous calculation of in-plane and out-of-plane birefringence associated with the selected position of the sample, as will be explained next. Used for.

As described above, the magnitude of the retardance of the normal incident light beam “B1” that can be regarded as being on the Z axis is represented by δ _N (nanometers). The in-plane birefringence is defined as follows.

Here, n _Y and n _X represent the refractive index of the sample on the orthogonal axis, the X axis, and the Y axis of the sample, respectively, perpendicular to the incident light beam. The variable “d” is the thickness of the sample, typically measured with a micrometer, and is therefore multiplied by 1000 here to meet the nanometer dimension of the delay measurement, which yields the formula ( The in-plane birefringence of 9) is obtained.

  Therefore, the measurement amount of the vertical delay characteristic (retardance) is related to the in-plane birefringence as follows.

Considering the situation of determining the value of out-of-plane (ie, vertical) birefringence in the XZ plane (again using the orthogonal coordinate system described above), the out-of-plane birefringence is expressed as Δn _V1 = n _Z n _X .

  As described above, the fast axis ρ of the sample is calculated as shown in Equation (8). What is needed here is that this information ensures that the measured components of the birefringence (fast) axis and birefringence (fast) axis of the sample are in a straight line. To that end, assuming that the angle “A” of the oblique angle beam “B2” is φ (30 degrees in this example) and the sample has an average refractive index of n, the internal correction of the sample is made. The incident angle (due to refraction) is:

  The delay characteristic (retardance) of the oblique angle is expressed by the following equation.

  Rearranging equations (10) and (11) yields:

  Combining both equations leads to the following equation:

  Ie

  The value is the out-of-plane (ie vertical) birefringence of the sample in the XZ plane, as calculated using the computer 90.

  If desired, the device of the present invention is used to determine out-of-plane birefringence for different vertical planes, which in the YZ plane (perpendicular to the XZ plane) of the sample is as follows.

  The sample 26 can be rotated in its XY plane, i.e., in order to perform out-of-plane birefringence measurements other than the one vertical plane described above, a third source module and detection module pair is used. Can be used.

  Note that when the in-plane birefringence is negligible compared to the oblique birefringence, the X-axis and the Y-axis coincide with the birefringence axes (fast axis and slow axis) and the birefringence measuring device is unnecessary. Should. In such a case, the out-of-plane birefringence is as follows:

3 and 4 show a diagram of another embodiment of the present invention and a block diagram of signal processing elements of the apparatus shown in FIG. 3, respectively. In this example, the out-of-plane birefringence is calculated in the same manner as described above, but a different arrangement example is used to determine the measurement results of the delay characteristics (retardance) of the vertical δ _N and the oblique δ _O described above. 2 is an example of a dual PEM, single detector.

  As shown in FIG. 3, the vertical source module 310 includes a light source 322, a polarizer 324 given a +45 degree directivity, and a PEM 326 given a 0 degree directivity.

  The vertical detection module 312 includes a second PEM 328 in which a modulation frequency different from the modulation frequency of the first PEM 326 is set. The second PEM 28 is given a 45 degree directivity. The vertical detection module 312 also includes a zero degree analyzer 330 and a detection device 332.

  As in the previous embodiment, a holder 28 for a transparent sample 26 is disposed between the source and detection modules.

  With continued reference to the vertical source module 310 and the detection module 312 shown in FIG. 3, the source module 322 is a He-Ne laser that receives polarized light with a wavelength of 632.8 nanometers. Each of the polarizer 324 and the analyzer 330 is a Gran-Thomson polarizer. In this embodiment, a Si photodiode detector 344 is used. Both PEMs 326, 328 are rod-shaped quartz glass models having two transducers. The transducer is attached to the quartz glass optical element with a soft bond material. In order to minimize the birefringence introduced into the optical element, only the transducer is installed in the PEM housing. The two PEMs 326, 328 have nominal resonant frequencies of 50 and 55 kHz, respectively, and are driven by a controller (not shown).

  As shown in FIG. 4, the electronic signal generated by the detection device 332 includes both “AC” and “DC” signals, each subjected to different processing. The AC signal is supplied to two lock-in amplifiers 340 and 342. Each lock-in amplifier demodulates the 1F signal supplied from the detection device 332 with reference to the basic modulation frequency (1F) of the PEM.

  The DC signal from the detection device 332 is received by the lock-in amplifier 340 after passing through the analog-digital converter and the low-pass electrical filter. The DC signal represents the average intensity of the light reaching the detection device 332. As will be described next, both the DC and AC signals need to be recorded with different PEM delay settings.

  The theoretical analysis based on the measurement of the birefringence properties of the sample 26 in this example is also based on the Mueller matrix analysis, and for this dual PEM, single detector example shown in FIGS. This will be described below.

  The Mueller matrix for each of the paired source and detection modules shown in FIG. 3 is shown below. A sample 26 in the present optical device having a magnitude of δ (here considered in a general sense rather than a vertical / oblique sense as described below) and a fast axis angle of ρ is It is expressed by the following formula.

  The Mueller matrices of the two PEMs (one in the source module and the other in the detection module, with delay axes oriented at ρ = 0 and 45 degrees, respectively) are as follows:

Where δ1 and δ2 are the time-varying phase delays of the source PEM (326 or 426) and detection PEM (328 or 428), δ1 = δ1 _o sinω ₁ t and δ2 = δ2 _o sinω ₂ t, and Where ω ₁ and ω ₂ are the modulation frequencies of the PEM, respectively, and δ 1 _o and δ 2 _o are the delay amplitudes of the two PEMs.

  If the Mueller matrix of the optical element in the apparatus shown in FIG. 3 is used, the light intensity reaching the detector (344 or 444) is obtained as follows.

Here, I ₀ is the light intensity after passing through the polarizer (324 or 424), and K is a constant representing the transmission efficiency of the optical system after passing through the polarizer.

  Sin δ1 and cos δ1 in equation (19) can be expanded as follows by the first type Bessel function.

Here, k is “0” or a positive integer, and J _{2k + 1} is a (2k + 1) -th order Bessel function.

Here, J ₀ is a 0th order Bessel function, and J _2k is a (2k) th order Bessel function.

  A similar expansion can be performed for sinδ2 and cosδ2.

  By substituting the expansion equations of sin δ1, cos δ1, sin δ2, and cos δ2 into equation (19) and handling only the second-order Bessel function, the following terms can be obtained.

  The first part of terms (3) and (4) can be used to determine the linear delay characteristics at low levels (π / 2, ie ¼ wavelength or less). The term (2) is used to determine a higher level (up to π or half wavelength) linear delay characteristics. The term (1) includes a DC term relating to the average light intensity.

  Using the lock-in amplifier (304, 342 or 440, 442) referenced in the associated first harmonic (1F) of the two PEMs to determine the 1F AC signal of the detection device (332 or 432) it can. The lock-in amplifier effectively eliminates the involvement of all other harmonics. The 1F signal measured by the lock-in amplifier for two PEMs is:

Individually √2 depends on the fact that the output of the lock-in amplifier measures the root mean square, not the amplitude. From equation (22), the maximum values of J ₀ (δ1 ₀ ) 2J ₁ ((δ2 ₀ ) and J ₀ (δ2 ₀ ) 2J ₁ ((δ1 ₀ )) indicate the best results for the output of the lock-in amplifier. When the AC signal is collected, the delay amplitude of both PEMs is set to 1.43 radians for the optimization of the AC signal.

  The DC signal is derived from the term (1) as follows.

  Here, all terms that change as a function of the modulation frequency of the PEM are omitted because they do not substantially contribute to the DC signal. The low pass electrical filter described above is used to eliminate such vibrations.

Within a small angular approximation (sinx = x and sin ² x = 0 when x is small), V _DC does not depend on the sample delay and thus represents the average value of the light intensity reaching the detector. However, when a sample with a delay in excess of 30 nm is measured, V _DC is generally affected by the magnitude and angle of the delay, as shown in equation (23). Therefore, the measured DC signal does not accurately represent the average light intensity. In this case, the simplest method is to set both J ₀ (δ1 ₀ ) and J ₀ (δ2 ₀ ) to “0”. The DC signal is as follows.

In this example, the delay amplitude of the PEM was selected to be δ1 ₀ = δ2 ₀ = 2.405 radians (0.3828 waves) for DC signal recording. In such a PEM setting, J ₀ (δ1 ₀ ) = J ₀ (δ2 ₀ ) = 0. Therefore, the DC signal does not depend on ρ or δ, but accurately indicates the average value of the light intensity reaching the detector (244 or 444).

As can be seen, this method requires AC and DC signals to be recorded at different PEM settings, and thus the measurement speed is low (approximately 2 seconds per data point). This method provides an accurate measurement of linear delay above 30 nm. Alternative methods can be used when speed is important. When a DC signal is collected at δ1 ₀ = δ2 ₀ = 0143 radians under conditions where an AC signal is recorded, the delay characteristics of the sample measured using the ratio of AC to DC depend on the angular orientation of the sample To do. However, the DC term is defined by equation (23). Therefore, it is possible to reduce the angular dependence of the delay characteristic by repeating the calculation of both the magnitude and angle of the delay characteristic.

  In order to eliminate the effects of light intensity fluctuations due to light source fluctuations and absorption, reflection and scattering from the sample and other optical elements, a ratio of 1F AC signal to DC signal is used. The ratio of the AC signal to the DC signal for both PEMs is expressed by equation (25).

As correction ratios for both PEMs, definitions of R ₁ and R ₂ are required.

  Finally, the magnitude of birefringence and its angular direction are expressed as follows.

  Here, δ is a scalar expressed in radians. When measurements are made at a specific wavelength (eg 632.8 nm), it is easy to convert the delay to nanometers (eg multiply by 632.8 / (2π)).

  It should be emphasized that equation (27) has been developed especially for small linear birefringence by using the arc sine function in the determination of linear birefringence. Therefore, the method described here has a theoretical upper limit of π / 2 or 158.2 nm when a 632.8 nm laser is used as the light source.

  The signal at both PEM modulation frequencies depends on the direction of the fast axis of the sample (see equation (24)), and the final delay magnitude does not depend on the fast axis angle (see equation (27)). In order to achieve independence of this angle with respect to the magnitude of the delay, it is important to correctly orient all optical elements in the device. Further, as in the above-described embodiments, even when high-quality optical elements are used, correction of residual linear birefringence (instrument correction) existing in the instrument itself is sensible.

The above in equation (27) is basically presented in a general sense, and if the detection information from the normal incident ray “B1” (FIG. 3) can be applied during the calculation, the implementation described above. One skilled in the art will appreciate that the in-plane delay measurement δ _N can be determined corresponding to the same measurement δ _N as described above in connection with the example.

The value of the delay δ _N caused by the in-plane birefringence of the sample in the embodiment of FIG. 3 is the delay measurement given by the other “oblique” ray shown as “B2” in FIG. Used simultaneously with detection of The light beam “B2” is directed obliquely to the surface of the sample 26. Thus, ray “B2” exits the sample with properties that provide information related to the delay that occurs along the (refractive) incidence path of ray “B2” passing through the sample. Thus, the information provided by the two angularly separated rays “B1”, “B2” is detected and provides the in-plane birefringence of the sample in addition to the in-plane birefringence of the sample 26. Receive processing accordingly.

  Except as noted below, the diagonal source module 314 and the diagonal detection module 316 are comparable to the vertical source module 310 and the vertical detection module 312 respectively. Accordingly, the diagonal source module 314 includes a light source 422, a polarizer 424, and a PEM 426 that function similarly to the light source 322, polarizer 324, and PEM 326 of the vertical source module 310. Similarly, the diagonal detection module 316 includes another PEM 428 and a detection device 432 that function similarly to the PEM 328 and detection device 332 of the vertical detection module 312.

  The fundamental difference between the vertical modules 310, 312 and the diagonal modules 314, 316 is that they pass through the sample 26 at an angle “A” in FIG. 3 that is oblique with respect to the normal incident light beam “B1”. It is used to provide and detect the propagating ray “B2”. For this purpose, the oblique source module 314 is installed to produce angularly separated rays “B1” and “B2” that propagate through the same location in the sample. In the example shown in FIG. 3, the angle “A” is selected to be 30 degrees.

In accordance with the above description of the vertical detection module 312 and associated processing, those skilled in the art will recognize that the detection signal applied to the lock-in amplifiers 440, 442 (FIG. 4) and processed by the computer 90 is the oblique beam “B2” (FIG. 3). measurement of influencing delay) [delta] _O (will appreciate that would result in nanometers). This information is preferably for simultaneous in-plane and out-of-plane birefringence calculations related to the selected location of the sample, as described above in connection with the embodiment of FIGS. And used with the measured value of the vertical delay δ _N.

  The embodiment described above included two separate source modules and corresponding two separate detection modules. As a replacement example, it is conceivable to use a single source module 510 as shown in FIG. In such an embodiment, the source module 510 has those comparable to each of the source module components (light source, PEM, etc.) of one of the aforementioned source modules, such as the vertical source module 10, so that Composed. The light beam “B” emitted from the source module enters a diverter 514 before reaching the sample on the holder 28. The shunt can be a partial reflector, and as shown in FIG. 5, the sample is reflected by a mirror 518 to intersect the beam portion “B1” that has passed through the shunt 514 at a common location on the sample. Redirect some rays to switch back to the reflected ray “B2”. Thus, the shunt 514 and the mirror 518 produce two angularly separated rays “B1” and “B2” that pass through the sample from the ray “B” of the single source module 510.

  After passing through the sample, the light beam “B1” (FIG. 5) is directed to the detection module 512. The module 512 compares them to each of the components (analyzer, detector, etc.) described in the detection module described above, such as the detection module 12 for detecting information related to in-plane birefringence. Including. Similarly, the light beam “B2” is directed to the oblique detection module 516 after passing through the sample 26. The module 516 also includes the components (analyzer, detector) described in the detection module, such as the detection module 16, for detecting information related to the oblique angular delay imparted to the beam "B2". Etc.) including those comparable to each other. As in the previous examples, the information gathered from the vertical and tilt detection modules is processed for in-plane and out-of-plane birefringence values of the vertical plane of interest.

  A flip mirror can be used as the shunt 514 in the embodiment of FIG. In this regard, the mirror periodically flips from the source module 510 into and out of the path of ray “B”, thereby producing the oblique ray “B2” for detection as described above. Therefore, when the flip mirror periodically exits the path of the light beam “B”, the vertical light beam “B1” reaches the detection module 512 as shown. The frequency of operation of the flip mirror detects both in-plane birefringence (which affects light beam B1) and out-of-plane birefringence (determined by detection information from both light beams B1 and B2) substantially simultaneously. It is preferably done at a high enough speed (as defined by an appropriate reciprocating actuator).

  FIG. 6 is another embodiment of the present invention, in order to generate two angularly separated rays “B1” and “B2” that pass through the sample 26, as in FIG. A source module 610, a shunt 616, and a mirror 618 are used. This embodiment includes another mirror 614 for reflecting the oblique light beam “B2” after passing through the sample. The reflected light beam strikes a converger 620, which is located in the optical path of the normal incident light beam B1, which terminates in a single detection module 612. The detection module 612 has elements comparable to the detection module described above, such as the detection module 312 of FIG.

  The converging device 620 allows the path of the normal incident light beam “B1” to reach the detection module 612 and the other light beam “B2” along the common axis for detection by the same detection module 612. To converge. Preferably, at least one of the shunt 616 or the converging unit is a flip mirror that enters and exits the path of the normal incident light beams “B” and “B1”. The actuator of the flip mirror is under the control and monitoring of the computer so that the device quickly hits a single detection module at a particular time of rays “B1” or “B2” in the convergent path Can be determined.

  Also, the sample holder can be configured to periodically tilt with respect to a single source beam traveling along a single (non-branching) path. Such tilting is similar to providing both the above-mentioned angularly separated rays as a sample enters and exits the tilted position, as shown by the wavy lines in FIG. It is possible to perform various functions. Preferably, the holder 28 is such that the light beam passes through the same position of the sample and that information is detected both as a normal incident beam (a flatly oriented sample) and a tilted incident beam (tilted sample). Arranged and operated to ensure that the sample is tilted.

  One embodiment of the tilted sample holder described above is shown in FIG. There, the tilted sample 236 traverses a fixed path of a ray 221 such as the ray emanating from the source module 10 as described above (here in the linear Y direction). The sample 236 is gradually traversed by the X / Y stage sample holder 234, and as a result, birefringence data over a plurality of positions on the sample surface is collected. The sample holder 234 is made to be able to rotate the sample, for example, to facilitate the analysis of the sample's birefringence at a number of different incident angles of the rays. For example, the holder 234 shown in FIG. 8 mounts the sample 236 around the aligned pivot posts 240, 241. A servo motor 235 is connected to one post or shaft 241 and is operable by the computer to rotate the sample to a desired angle for analysis. In one embodiment, the servo motor includes an encoder that provides position information of the shaft 241 to the computer. The servo motor 235 can be driven to rotate the sample 236 from the angular direction indicated by the solid line in FIG. 8 to the horizontal position indicated by the broken line 243.

  In certain optical applications, it is desirable to use light with a very short wavelength, such as a wavelength of about 157 nanometers, such wavelength being referred to as deep ultraviolet or DUV. It is therefore important to accurately characterize the optical elements used in an optical system or apparatus that uses DUV light. Such elements include, for example, scanner or stepper calcium fluoride (CaF2) lenses. Birefringence or retardance is one such characteristic of the optical element. Since the optical element retardance is a property of the optical material and the wavelength of light passing through the material, an apparatus for measuring the optical element retardance used in a DUV optical apparatus accurately detects the DUV optical signal. In order to process, it must work with a DUV light source and associated components.

One problem associated with the use of DUV light for applications such as birefringence measurements is the absorption of DUV light by the appearance of oxygen in the device environment, particularly in the light path. In this regard, oxygen molecules (as well as other contaminants such as water vapor or trace carbohydrates) absorb DUV light and, as a result, attenuate the light and are required to make an accurate birefringence measurement of the sample. Will reduce the signal. One way to remove oxygen (as well as other contaminants) from the device environment is to drive it out of the device or light path with nitrogen (N ₂ ).

  The tilted sample holder shown in FIG. 7 is considered to be used in an apparatus that requires an oxygen purge light path. Accordingly, the apparatus is provided with a telescopic upper purge gas outlet tube 254 as schematically shown in FIGS. A lower purge gas lead-out pipe 256 that is similarly extendable and retractable is provided under the sample.

  The gas pressure supplied to the tubes 254, 256 is selected such that the purge gas exiting the tubes exerts a positive pressure on the gap interposed between the tubes and the sample surface, thereby causing the light of the DUV light beam 221 to light. Oxygen can be prevented from entering the path.

  7A to 7C show how the upper gas outlet tube 254 contracts and the lower gas outlet tube 256 as the sample 236 crosses from the left to the right in the drawing. Is shown to stretch. From the figure, the ends of the two purge gas outlet pipes are maintained close to the surface of the sample, so that the gap interposed between the pipe and the sample is at the positive pressure of the purge gas flowing out of the two pipes. You will see that it is retained.

  Referring to FIG. 8, adjustable purge gas lines 254 and 256 can be configured in any manner. In one embodiment, the telescopic upper tube 254 is provided protruding from the normally sealed volume top wall 105 in which the sample 236 and holder 234 reside. Supply pipe 258 delivers pressurized purge gas from a remote source.

  The extension 260 of the upper tube 254 is connected to a linear actuator 262 mounted adjacent to the tube 254. The actuator 262 is operable to extend and retract the connected extension 260 in two opposite directions, indicated by arrows 264 in FIG. The lower telescopic tube 256 is similarly expanded and contracted by a linear actuator 263 under computer control.

  The sample holder 234 can be configured to hold the sample 236 at a specific angle with respect to the incident light beam 221. In such an example, the linear actuator is controlled such that as the sample is traversed, the ends of the tubes 256, 254 are held close to the respective surfaces of the sample. For example, in FIG. 7, the linear actuator gradually contracts the upper 254 and gradually extends the lower tube 256 as the sample crosses from left to right in the figure. Get control.

  One skilled in the art will appreciate that the effect of tilting the sample from a horizontal plane is that it can change the path of rays that propagate through the sample. For example, as shown in FIG. 9, a vertical (ie, 0 degree incident angle) impinging on an optical element or sample 402 (here, sample 402 oriented horizontally as shown by the solid line). An “impinging” (collision) path 400 of rays exits the sample in alignment with an “emanating” (emission) path whose axis is aligned with the impinging path 400. Thus, the ray follows this path 404 to the next optical element 406 of the device.

  In the example where the sample 402 is tilted at an angle θ (as indicated by the dashed line in FIG. 9), the ray emulating path 404 is displaced from the impinging path by a distance “D”. The magnitude of this displacement “D” is a function of the refractive index, thickness, and tilt angle θ of the sample.

  In some birefringence measuring devices, it is desirable to measure birefringence with high spatial resolution across the sample. Therefore, relatively small apertures are used in the device to achieve small beam size and corresponding high resolution. For example, the small diameter aperture can be placed in close proximity to a detector that receives light traveling from the sample along the emanating path 404.

  In such an apparatus, a mechanism is used to tilt the sample and apply the displacement “D” described above to the beam emanating path 404, so that the optical element of the emanating path 404 is displaced. It is important in terms of the subsequent signal processing described above that it is constructed and arranged to receive the Ting beam (or at least the part suitable for use of the beam). One way to accomplish this is to place an aperture of the beam diameter dimension in the ray impinging path 400 to ensure that such an aperture is not affected by the displacement of the ray.

  In addition, since the maximum shake amount “D” can be determined in advance, the optical device captures a portion suitable for use of the displaced emanating beam path regardless of the amount of displacement of the emanating beam path. An opening with sufficient dimensions can be provided in the emanating beam path. In this regard, a light source that diverges slightly is preferred. The portion of the captured beam that is suitable for use as described above has a very low intensity compared to the entire beam, but this low-intensity assessment is sufficient for accurate measurements. For example, the ratio of the detected AC (modulated) signal to the DC (average) signal is used to determine the retardance under a situation where the detected light intensity varies.

  When the sample is tilted about a single axis (as described in connection with FIGS. 7 and 8), the displacement of the emanating beam path 404 is substantially linear and the single axial direction It is. Taking this unidirectional displacement into consideration, the rectangular opening is close to the detector (ie, toward the working surface of the detector) and the long side of the opening is the direction in which the light beam is displaced (“Y” axis in FIG. 7). ) And can be used in parallel with the axis along the line. Such an aperture is useful to limit the amount of undesired non-parallel rays reaching the detector.

  In the embodiment described in connection with FIG. 3, the PEM is one of the optical elements through which the light beam exiting the sample passes, so that the light beam exiting the sample undergoes additional phase modulation. Accordingly, element 406 in FIG. 9 is considered a PEM for the purposes described below.

  The magnitude of the delay introduced by the oscillating PEM 406 into the emanating (emitted) beam 404 varies somewhat depending on the amount of displacement “D” of the emanating beam from a predetermined position on the optical element of the PEM. . For example, when the optical element of the PEM (indicated by reference numeral 408 in FIG. 9) is installed between two transducers 410 and driven by both transducers, it is applied to a light beam that passes through the center of the optical element 408. The amount of delay that is applied is slightly larger than the delay imparted to rays that are displaced from the center by an amount “D”.

  As noted above, the amount of run-out “D” is easily determined, and the amount of delay change imparted by the PEM 406 is important (the “error” amount), and this error is determined and used in the appropriate equation described above. Can do. For example, due to the length “L” of PEM optical element 408 (between both transducers 410) and the beam displacement “D”, the amount of delay error will be a function of the ratio 2D / L.

  It is also contemplated that the error can be determined empirically for various increments of “D” and can be stored in a firmware lookup table related to general signal processing. Information about the angular position of the sample holder (resulting from the servo motor and encoder device described above) can be used in the computer controlling for the determination of the current displacement “D”, and the current displacement is It can be used to refer to the look-up table leading to the related delay error.

  Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made without departing from the teachings and spirit described above.

1 is a view showing an example of a suitable optical apparatus used for measuring out-of-plane birefringence according to the present invention. FIG. 2 is a block diagram of signal processing elements of the apparatus shown in FIG. 6 is a drawing of another embodiment showing another optical apparatus for measuring out-of-plane birefringence according to the present invention. FIG. 4 is a block diagram of signal processing elements shown in FIG. 3. 4 is a drawing of another optical device for measuring out-of-plane birefringence according to the present invention. 4 is a drawing of still another optical device for measuring out-of-plane birefringence according to the present invention. It is a 3 part drawing which shows the Example which the sample sample which consists of an optical element with which inclination, ie, an inclination direction, moves about a light path. FIG. 8 is an enlarged view showing the details of the embodiment of FIG. 7 showing the movement of the purge gas outlet tube with respect to the movable tilted sample. 2 is a drawing showing the tilt of an optical element and its effect on the beam path of the sample.

Explanation of symbols

10, 310 Vertical source module 12, 312, 512, 612 Vertical detection module 14, 314 Diagonal source module 16, 316, 516 Diagonal detection module 20, 220, 322, 422 Light source 22, 222, 324, 424 Polarizer 24 Optical element 25, 225, 326, 328, 426, 428 Photoelastic Modulator (PEM)
26, 236 Sample 28, 234 Sample holder 30, 230 Beam splitting mirror 32, 50, 232, 250, 332, 432 Detector 42, 74, 330, 430 Analyzer 44, 76, 344, 444 Detector (photodiode)
77 Filter 84 Controller 80, 280, 340, 342, 440, 442 Lock-in amplifier 90 Computer 510, 610 Single source module 512 Single detection module 514, 616 Shunt 518, 618 Mirror 620 Concentrator

Claims (26)

A method for determining out-of-plane birefringence of a transparent sample,
Generating two rays that are angularly separated from each other;
Phase-modulating each of the two angularly separated beams and then passing through a location in the sample;
Then phase modulating each ray;
Detecting characteristics of the two rays that have undergone phase modulation after passing through the position;
Using the detected property to calculate out-of-plane birefringence of the sample.   The method of claim 1, wherein the two rays make an angle of about 30 degrees.   The method of claim 1, wherein the passing step includes providing two light sources that are spaced apart from each other to generate the two rays.   The method of claim 1, comprising using a photoelastic modulator for the phase modulation.   The method of claim 1, comprising using a photoelastic modulator to phase modulate each light beam after passing through the sample.   The method of claim 1, wherein the sample has an output surface and includes directing one of the angularly separated rays to an angle of incidence perpendicular to the output surface.   The detection step of claim 1, comprising separating each light beam into two parts after each light beam has passed through the sample and directing each part of the beams to a separate detector. the method of.   The passing step includes providing a single light source for generating a first light beam and branching the first light beam to provide the two light beams that are angularly separated. The method of claim 1.   9. The method of claim 8, wherein the branching step includes sequentially branching at least a portion of the first light beam to provide the two light beams that are angularly separated.   9. The method of claim 8, wherein the branching step includes periodically splitting the first light beam to provide the two light beams that are angularly separated.   9. The method of claim 8, comprising providing a detector for receiving each light beam that has been angularly separated after passing through the sample.   The method of claim 8, comprising converging the two rays after the two rays that are angularly separated from each other pass through the sample.   The method of claim 12, wherein the converging step includes directing the two rays along a common axis after the two angularly separated rays pass through the sample.   14. The method of claim 13, comprising using a single detector that detects the characteristics of the light that has passed through the sample.   The method of claim 9, comprising using two detectors to simultaneously detect the characteristics of the two rays that have passed through the sample.   Periodically moving the sample such that the angularly separated light beams are directed toward a plurality of positions on the sample; and out-of-plane birefringence at the plurality of positions of the sample. The method of claim 1 including the step of calculating.   The method of claim 1, comprising directing the two angularly separated rays into a first plane with respect to a predetermined axis of the sample.   18. The method of claim 17, comprising periodically changing the position of both rays by changing the position of the first surface with respect to the sample axis.   The method of claim 1, wherein the passing step includes tilting the sample.   The method of claim 1, comprising rotating the sample and recalculating the out-of-plane birefringence at the position of the sample.   The method of claim 1, comprising calculating in-plane birefringence at the location of the sample in addition to calculating out-of-plane birefringence at the location within the sample.   The method of claim 1, comprising calculating the in-plane birefringence at the position simultaneously with calculating the out-of-plane birefringence at the position of the sample.   The method of claim 1, comprising using the detected characteristic of one ray to define a fast axis of the in-plane birefringence of the sample. An optical device for measuring out-of-plane birefringence of a transparent sample,
At least one light source;
A branching means associated with the light source for directing two angularly separated rays to a common location in the sample;
Means for modulating the phase of each ray and then passing the two angularly separated rays through the common location in the sample;
Means for modulating the phase of each ray after passing through the common position;
An optical device comprising: detecting means for detecting characteristics of the two light beams which have passed through the position and thereafter undergo phase modulation for use in calculating the out-of-plane birefringence of the sample.   25. The optical apparatus according to claim 24, further comprising converging means for directing the two light beams angularly separated to a common axis after passing through the sample.   25. The optical apparatus according to claim 24, comprising processing means for performing in-plane and out-of-plane birefringence processing at the position of the sample substantially simultaneously. "

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