3-Layer Spherical Lens Focal Plane Mapping - Revision history

Greg at 19:46, 3 August 2017

2017-08-03T19:46:42Z

Greg at 19:27, 3 August 2017

2017-08-03T19:27:24Z

Greg: Greg moved page Mapping Focal Plane to 3-Layer Spherical Lens Focal Plane Mapping: Initial title was clumsy

2017-08-03T19:13:41Z

Greg moved page Mapping Focal Plane to 3-Layer Spherical Lens Focal Plane Mapping: Initial title was clumsy

Greg: /* Resolving Shift */

2017-08-03T12:55:28Z

‎Resolving Shift

Greg: /* Measurements with Tilted Lens */

2017-08-03T12:44:39Z

‎Measurements with Tilted Lens

Greg: /* Initial Results */

2017-08-03T12:42:37Z

‎Initial Results

Greg: /* Initial Results */

2017-08-03T12:41:46Z

‎Initial Results

Greg: /* Measurement */

2017-08-03T12:39:35Z

‎Measurement

Greg: /* Setup */

2017-08-03T12:38:22Z

‎Setup

Greg: /* Resolving Shift */

2017-06-13T21:32:11Z

‎Resolving Shift

@@ Line 1: / Line 1: @@
-A novel 3-layer spherical lens has been designed for the [https://eic.jlab.org/dirc/index.php/Main_Page Detection of Internally Reflected Cherenkov light (DIRC)] detector system to be used for the EIC. Simulation predicts the shape of the focal plane of the new 3-layer lens design for the DIRC@EIC to be relatively flat, providing better focusing at the detector plane of the DIRC detector. A laser setup was built at Old Dominion University (ODU) to measure the focal plane of a prototype lens and verify the shape and position.
+A novel 3-layer spherical lens has been designed for the [https://eic.jlab.org/dirc/index.php/Main_Page Detection of Internally Reflected Cherenkov light (DIRC)] detector system to be used for the EIC. The lens consists of two layers of fused silica sandwiching a thin layer of [https://refractiveindex.info/?shelf=glass&book=SCHOTT-LaK&page=N-LAK7 lanthanum crown glass NLaK33]. The figure below shows two photos of a prototype lens built for testing purposes as well as the dimensions of the lens. Simulation predicts the shape of the focal plane of the new 3-layer lens design for the DIRC@EIC to be relatively flat, providing better focusing at the detector plane of the DIRC detector. A laser setup was built at Old Dominion University (ODU) to measure the focal plane of the prototype lens and verify the shape and position.
-[[File:3CS_Schematic.png | thumbnail | center | 600px | Photos of the prototype 3-layer lens (top), and an exploded view showing the dimensions of each component (bottom).]]
+[[File:3CS_Schematic.png | thumbnail | center | 600px | Photos of the prototype 3-layer lens (a), and an exploded view showing the dimensions of each component (b).]]
 == Simulation ==
-GEANT4 simulation package can be found here [https://github.com/hyperbolee/prtdirc].
+The GEANT4 simulation package can be found here [https://github.com/hyperbolee/prtdirc].
-To run lens measurement simulation for 3-layer lens:
+The following is used to run the simulation for the focal plane:
 <code>
@@ Line 14: / Line 14: @@
 == Setup ==
-The setup built at ODU (shown below) uses a 530 nm green laser that shines through a 50/50 beam splitter and a mirror to make two parallel beams with a 1 mm separation. The beams pass through a 30x40x60 cm<sup>3</sup> glass fish tank filled with Britol 9NF White Mineral Oil with a refractive index similar to that of fused silica. The beams pass through the 3-layer prototype lens, being held in place by a 3D printed holder which rotates in one plane (called the tilt angle) and is attached to a rotation table on top of the tank that rotates in a perpendicular plane (called &theta;, or the polar angle). The beams are then focused onto a plastic screen inside the tank that is attached to a sliding track and allowed to move freely.
+The setup built at ODU (shown below) uses a 530 nm green laser that shines through a 50/50 beam splitter and a mirror to make two parallel beams with a 1 mm separation. The beams pass through a 30x40x60 cm<sup>3</sup> glass tank filled with Britol 9NF White Mineral Oil with a refractive index similar to that of fused silica. The beams then pass through the prototype lens, being held in place by a special 3D printed holder which rotates in one plane (called the tilt angle) and is attached to a rotation table on top of the tank that rotates in a perpendicular plane (called &theta;, or the polar angle). The beams are then focused onto a plastic screen inside the tank that is attached to a sliding track and allowed to move freely. The focal distance is measured from the edge of the lens closest to the screen.
 [[File:Lens setup schematic.png | thumbnail | center | 600px | Illustration of ODU laser setup (left) and a zoom-in of the lens holder and plastic screen (right).]]
@@ Line 22: / Line 22: @@
 [[File:Lasertest1.jpg | thumbnail | center | 350px | ODU setup showing lasers on and focusing on the screen.]]
-== Measurement ==
+== Measurements ==
-Initial measurements were taken with a 632 nm red helium-neon laser, but the beam spot was too large and distorted, so the 530 nm green laser was used instead. Beams initially had a separation of 5 mm but were reduced to 1 mm in an effort to reduce effects from aberrations. In order to map the full focal plane for a fixed tilt angle the lens was rotated along the polar angle through up to 50&deg; in 2&deg; increments. Measurements were recorded at each step.
+Initial measurements were taken with a 632 nm red helium-neon laser, but the beam spot was too large and distorted, so it was replaced by the 530 nm green laser. Beams initially had a separation of 5 mm but were reduced to 1 mm in an effort to reduce effects from aberrations. In order to map the full focal plane for a fixed tilt angle the lens was rotated through a polar angle of between 0&deg; and 50&deg; in 2&deg; increments. Measurements were recorded at each step.
-To compensate for the finite size of the beams and the poor resolution of the human eye a method of averaging was used (illustrated in the figure below) in order to record a more accurate and consistent focal point. Measurements were taken at the point where the beams seem to first converge and again where they first seem to diverge. The average position of these two points lead to a much more consistent measurement and better results.
+To compensate for the finite size of the beams and the poor resolution of the human eye, a method of averaging was used (illustrated in the figure below) in order to record a more accurate and consistent focal distance. Measurements were taken at the point where the beams seem to first converge and again where they first seem to diverge. The average position of these two points was recorded as the proper focal distance, and lead to a much more consistent measurement and better results.
 [[File:Laser_crossing.png| frame | center | Illustration of two beams of finite size crossing. Any point between the two red circles could be seen as a "focal point" to the human eye, so the average position between these two points is taken to be the focal point.]]
 == Initial Results ==
-Initial measurements were taken with a 5 mm separation between beams and a lens holder that allowed rotation around the center of the lens. The results, shown below, were much more curved than expected from simulation. The first thought was to narrow the beams to a 2 mm, and finally 1 mm separation, but results were similar.
+Initially the lens holder was designed such that center of the lens was fixed when rotating through the polar angle. The results, shown below, were much more curved than expected from simulation. The first thought was to narrow the beams to a 2 mm, and finally 1 mm separation, but results were similar.
 [[File:Focalplane initial.png | thumbnail | 500px | center | Initial results of measurements with 5 mm beam separation and center-rotated lens holder.]]
-It was then deduced that in the simulation the beams always pass through the same point on the lens surface while, due to the rotation of the holder, they were passing through different points in the ODU setup (illustrated below). A new lens holder was printed to compensate for this difference.
+It was then deduced that in the simulation the beams always pass through the same point on the lens surface while, due to the rotation of the holder, they were passing through different points in the ODU setup (illustrated below). A new lens holder was printed such that the lens rotated about its edge to compensate for this difference.
 [[File:Lens rotation point.png | thumbnail | 350px | center | Illustration of the discrepancy between beam positions in data (black) and simulation (yellow) in relation to the original beam positions (blue) for a given rotation point
 (red) at the center (top) of the lens, or at the edge (bottom) of the lens.]]
-Another round of measurements showed that the original flat shape of the focal plane was recovered when using the new holder. The shape of the plane measured with the original holder was also compared to a modified version of the simulation that took the movement of the beams into account, and again the shape was very nicely reproduced. There is still a systematic shift in the absolute position of the focal plane of ~4cm, which will be addressed later in this article.
+Another round of measurements showed that the original flat shape of the focal plane was recovered when using the new holder. The shape of the plane measured with the original holder was also compared to a modified version of the simulation that took the movement of the beams into account, and again the shape was very nicely reproduced. There was, however, still a systematic shift in the absolute position of the focal plane of ~4cm, which will be addressed later in this article.
 [[File:Focalplane corrections.png | thumbnail | 500px | center | Results of measurements of focal plane with lens rotating around its center (a) and its edge (b) after printing a new holder.]]
 === Measurements with Tilted Lens ===
-Because the lens holder allows for a secondary plane of rotation (the tilt angle) the full 3D focal plane can be mapped. Below is a plot of the measured and simulated focal plane of 3-layer lens for 0&deg;, 5&deg;, 10&deg;, and 20&deg; tilt angles. For 0&deg; and 10 &deg; the full plane was mapped for both positive and negative polar angles for sanity checks, while at 5&deg; only a few points were selected, and at 20&deg; tilt the beams were already too distorted for a proper measurement so no negative polar angles were measured. Again, the laser data nicely reproduces the simulation's shape, neglecting the 4 cm shift, up to 10&deg; tilt, while going to larger tilts the finite size of the beams lead to too much distortion, making measurements unreliable and inaccurate.
+Because the lens holder allows for a secondary plane of rotation (the tilt angle), the full 3D focal plane can be mapped. Below is a plot of the measured and simulated focal plane of 3-layer lens for 0&deg;, 5&deg;, 10&deg;, and 20&deg; tilt angles. For 0&deg; and 10 &deg; the full plane was mapped for both positive and negative polar angles for sanity checks, while at 5&deg; only a few points for the negative polar angles were selected, and at 20&deg; tilt the beams were already too distorted for a proper measurement so no negative polar angles were measured. Again, the laser data nicely reproduces the simulation's shape, neglecting the 4 cm shift, up to 10&deg; tilt, while going to larger tilts the finite size of the beams lead to too much distortion, making measurements unreliable and inaccurate.
 [[File:Focalplane all tilts.png | thumbnail | 1000px | center | Measured (circles) and simulated (lines) focal plane of 3-layer lens for 0&deg; (red), 5&deg; (green), 10&deg; (blue), and 20&deg; (purple) tilt angles.]]
 == Error Evaluation ==
-To evaluate the error associated with the position of the focal point 10 measurements each were done at 0&deg; and 10&deg; polar angle rotation one after another to get the standard deviation of the measured positions. This resulted in a 0.29 cm uncertainty.
+To evaluate the error associated with the position of the focal point, 10 measurements were done at both 0&deg; and 10&deg; polar angle rotation one after another to get the standard deviation of the measured positions. This resulted in a 0.29 cm uncertainty.
 The uncertainty in the angle of the rotation table was assumed to be 1&deg; as multiple alignments were done to set the lens to a "zero" position which resulted in a maximum deviation of 1&deg;. The actual uncertainty in the rotation angle is likely much smaller.
-== Resolving Shift ==
+== Understanding the Systematic Shift ==
-Several contributions were considered for explaining the 4 cm systematic shift of the focal plane position: a smaller radius of the second curved surface of the lens than was stated in the spec sheet, a larger refractive index of the NLaK33 glass layer, a smaller index of refraction of the mineral oil than was expected, or a small converging angle of the beams off parallel could all explain this shift.
+Several contributions were considered for explaining the 4 cm systematic shift of the focal plane position: <b>a)</b> a smaller radius of the second curved surface of the lens than was stated in the spec sheet, <b>b)</b> a larger refractive index of the NLaK33 glass layer, <b>c)</b> a smaller index of refraction of the mineral oil than was expected, or <b>d)</b> a small converging angle of the beams off parallel could all explain this shift.
 The following plot shows the effect on the focal plane when changing each of these quantities such that the 0&deg; tilt and 0&deg; polar angle point matches that of the laser data (necessary changes shown in table).
@@ Line 81: / Line 81: @@
 of the laser beams of 0.15 mrad (black). Experimental data is shown in red.]]
-The fact that the necessary change of the oil refractive index gives such a distorted shape rules out this possibility, while the very large deviation from the spec sheet of the refractive index of NLaK33 makes this option highly unlikely. To test the two remaining possibilities, a measurement of the focal plane with the beams off-center of the lens, shifted by 7 mm in the direction of a line connecting the two beams, was done and compared to simulation for both cases.
+The fact that the shift needed for the oil refractive index gives such a distorted shape rules out this possibility, while the very large deviation from the spec sheet of the refractive index of NLaK33 makes this option highly unlikely. To test the two remaining possibilities, a measurement of the focal plane with the beams off-center of the lens, shifted by 7 mm, was done and compared to simulation for both cases.
-As shown in the plot below, the assumption of a converging beam angle agrees very nicely with the data, while the assumption of the smaller radius is too far shifted to describe the data.
+As shown in the plot below, the assumption of a converging beam angle agrees very nicely with the data, while the assumption of the smaller radius is too far shifted.
 [[File:Focal plane xshift.png | thumbnail | 500px | center | 7 mm shift of the beams off-center from the lens for data (red) and simulation assuming a decreased radius of the second curved surface (blue) and a converging beam angle of 0.1 mrad (green).]]

← Older revision		Revision as of 19:27, 3 August 2017
Line 1:		Line 1:
−	Simulation predicts the shape of the focal plane of the new 3-layer lens design for the DIRC@EIC to be relatively flat, providing better focusing at the detector plane of the DIRC detector. A laser setup was built at Old Dominion University (ODU) to measure the focal plane of a prototype lens and verify the shape and position.	+	A novel 3-layer spherical lens has been designed for the [https://eic.jlab.org/dirc/index.php/Main_Page Detection of Internally Reflected Cherenkov light (DIRC)] detector system to be used for the EIC. Simulation predicts the shape of the focal plane of the new 3-layer lens design for the DIRC@EIC to be relatively flat, providing better focusing at the detector plane of the DIRC detector. A laser setup was built at Old Dominion University (ODU) to measure the focal plane of a prototype lens and verify the shape and position.
		+
		+	[[File:3CS_Schematic.png \| thumbnail \| center \| 600px \| Photos of the prototype 3-layer lens (top), and an exploded view showing the dimensions of each component (bottom).]]

	== Simulation ==		== Simulation ==

@@ Line 52: / Line 52: @@
 == Resolving Shift ==
-Several contributions were considered for explaining the 4 cm systematic shift of the focal plane position. A smaller radius of the second curved surface of the lens than was stated in the spec sheet, a larger refractive index of the center layer, a smaller index of refraction of the mineral oil than was expected, and a small converging angle of the beams off parallel could all explain this shift.
+Several contributions were considered for explaining the 4 cm systematic shift of the focal plane position: a smaller radius of the second curved surface of the lens than was stated in the spec sheet, a larger refractive index of the NLaK33 glass layer, a smaller index of refraction of the mineral oil than was expected, or a small converging angle of the beams off parallel could all explain this shift.
-The following plot shows the effect of focal plane when changing each of these quantities such that the 0&deg; tilt and 0&deg; polar angle point matches that of the laser data (necessary changes shown in table).
+The following plot shows the effect on the focal plane when changing each of these quantities such that the 0&deg; tilt and 0&deg; polar angle point matches that of the laser data (necessary changes shown in table).
 {| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

@@ Line 44: / Line 44: @@
 Because the lens holder allows for a secondary plane of rotation (the tilt angle) the full 3D focal plane can be mapped. Below is a plot of the measured and simulated focal plane of 3-layer lens for 0&deg;, 5&deg;, 10&deg;, and 20&deg; tilt angles. For 0&deg; and 10 &deg; the full plane was mapped for both positive and negative polar angles for sanity checks, while at 5&deg; only a few points were selected, and at 20&deg; tilt the beams were already too distorted for a proper measurement so no negative polar angles were measured. Again, the laser data nicely reproduces the simulation's shape, neglecting the 4 cm shift, up to 10&deg; tilt, while going to larger tilts the finite size of the beams lead to too much distortion, making measurements unreliable and inaccurate.
-[[File:Focalplane all tilts.png | thumbnail | 1000px | center | Measured (circles) and simulated (lines) focal plane of 3-layer lens for 0&deg; (red), 5&deg; (green), 10&deg; (blue), and 20&deg (purple); tilt angles.]]
+[[File:Focalplane all tilts.png | thumbnail | 1000px | center | Measured (circles) and simulated (lines) focal plane of 3-layer lens for 0&deg; (red), 5&deg; (green), 10&deg; (blue), and 20&deg; (purple) tilt angles.]]
 == Error Evaluation ==

@@ Line 32: / Line 32: @@
 [[File:Focalplane initial.png | thumbnail | 500px | center | Initial results of measurements with 5 mm beam separation and center-rotated lens holder.]]
-It was then deduced that in the simulation the beams always pass through the same point on the lens surface while, due to the rotation of the holder, they were passing through different points in the ODU setup (illustrated below). A new lens holder was printed to compensate for this difference. Another round of measurements showed that the original flat shape of the focal plane was recovered when using the new holder. The shape of the plane measured with the original holder was also compared to a modified version of the simulation that took the movement of the beams into account, and again the shape was very nicely reproduced. There is still a systematic shift in the absolute position of the focal plane of ~4cm, which will be addressed later in this article.
+It was then deduced that in the simulation the beams always pass through the same point on the lens surface while, due to the rotation of the holder, they were passing through different points in the ODU setup (illustrated below). A new lens holder was printed to compensate for this difference.
 [[File:Lens rotation point.png | thumbnail | 350px | center | Illustration of the discrepancy between beam positions in data (black) and simulation (yellow) in relation to the original beam positions (blue) for a given rotation point
 (red) at the center (top) of the lens, or at the edge (bottom) of the lens.]]
 [[File:Focalplane corrections.png | thumbnail | 500px | center | Results of measurements of focal plane with lens rotating around its center (a) and its edge (b) after printing a new holder.]]

← Older revision	Revision as of 19:13, 3 August 2017
(No difference)

@@ Line 83: / Line 83: @@
 [[File:Focal plane xshift.png | thumbnail | 500px | center | 7 mm shift of the beams off-center from the lens for data (red) and simulation assuming a decreased radius of the second curved surface (blue) and a converging beam angle of 0.1 mrad (green).]]
-A second shift of the converging angle was checked for both 0&deg; and 10&deg; as well as the 7 mm off-center shift such that instead of the (0&deg;,0&deg;) point from data aligning with simulation, the simulation gave a more averaged description of the data. This was achieved with a 0.1 mrad converging angle. This explanation is the most reasonable in describing the shift of the focal plane position, as the numbers on the spec sheet for the prototype lens are unlikely to be so far off, and such a small angle leads to only a 1 mm change in distance over 10 meters, which is imperceptible with out current setup at ODU.
+A second shift of the converging angle was checked for both 0&deg; and 10&deg; as well as the 7 mm off-center shift such that instead of the (0&deg;,0&deg;) point from data aligning with simulation, the simulation gave a more averaged description of the data. This was achieved with a 0.1 mrad converging angle. This explanation is the most reasonable in describing the shift of the focal plane position, as the numbers on the spec sheet for the prototype lens are unlikely to be so far off, and such a small angle leads to only a 1 mm change in distance over 10 meters, which is imperceptible with our current setup at ODU.
 [[File:Beam converge 0.1mrad.png | thumbnail | 500px | center | upright=0.85 | Comparison of 0&deg; tilt (red), 10&deg; tilt (green), and 7 mm shift of beams (blue) with data (circles) and simulation (lines) using an assumption of 0.1 mrad beam deviation from parallel.]]