Peterson xBSM Optics, Beam Size Calibration1 xBSM Beam Size Calibration Dan Peterson CesrTA general meeting introduction to the optics elements introduction to the x-ray energy distribution program for determining the x-ray energy distribution beam size range of usefulness of the optics the problem with taking more data

Peterson xBSM Optics, Beam Size Calibration2 There are two optics elements: “Pinhole”, “Slit”, “Gap” a single slit, or one dimensional pinhole image is characteristic of a single slit diffraction pattern the opening is optimized to provide the minimum image size for a point source larger opening broadens the image because it becomes a projection smaller opening broadens the image because of diffraction. Coded Aperture - array of slits, size varies light passing through different slits interferes, the mask has transparency >0, with phase shift, modifying the interference pattern and providing sharp features in the image With either optics element, The calibration of the image to measure the beam size requires a determination of the image for a point source; the image for any other beam shape is a convolution with this point source shape (or size). The determination of the point source image is dependent on a determination of the x-ray energy distribution.

Peterson xBSM Optics, Beam Size Calibration3 So, we must determine the x-ray energy distribution this depends on the generated distribution and the effects of the various filters placed in the beam line: the silicon substrate of the coded aperture, (known) any filters used, e.g. 4 μm diamond, (known) absorbing materials in the detector, (sort of known ) and the energy dependent efficiency of the detector. (not well known) I take generated energy dependent intensity distribution from Jackson: δI(ω)/δΩ| θ=0 = 3/(2π) e 2 /c γ 2 ω/ω c exp( -2ω/ω c ) (Jackson 14.88) This is the energy distribution in the synchrotron plane, and is valid if the light cone is wide compared to the optics element. The critical angle is θ c = 1/γ (ω/ω c ) -1/3 (Jackson 14.89) for the highest beam energy used with the low-energy coded aperture, 2.3 GeV, γ = 4501, for a high x-ray energy at this beam energy, 7.5 keV, ω/ω c = thus, the smallest critical angle to be considered is θ c = 1.4 x radians. The full height at the optic corresponding to this angle is, θ c * 2 * ObjectDistance = 1200 μm. The height of the Coded Aperture is 300 μm (600 μm including extra interfering sidebands), so the equation for energy spectrum on the orbit plane is valid

Peterson xBSM Optics, Beam Size Calibration4 The diamond filter low energy cut-off (50% of high energy transmission) is at about 1.6 keV. The molybdenum filter has a peak at 2.5 keV, but also passes the highest energy x-rays. While the Jackson formula is valid for the production distribution, we do not know much about the effect of the detector. We can place various filters in the beam line to probe the relative x-ray intensity in various energy ranges. The aluminum filter has a peak at 1.5 keV, but also passes the high energy x-rays. The silicon filter is the substrate of the coded aperture

Peterson xBSM Optics, Beam Size Calibration5 pinhole image relative integrated area (normalized to constant pinhole slit width) (normalized to particle beam current) {model} in red Jackson formula, without any modification data in black no filter 4 μm diamond filter 2 μm molybdenum filter GeV { } { } { } GeV 1 { 1 } { } { } GeV --- { } { } { } April 2012 Total intensity measurements were taken with 3 beam energies and 3 filter conditions. (Not all combinations were recorded.) A constant size pinhole was used. The table shows the comparison between the data and model for the relative total intensity. The unknown properties of the detector have a large effect. E0E0

Peterson xBSM Optics, Beam Size Calibration6 pinhole image relative integrated area (normalized to constant pinhole slit width, particle beam current) average x-ray energy in blue {model} in red Jackson formula, with applied transmission: (E x-ray ) 2.31 data in black no filter 4 μm diamond 7.2 μm aluminum 2 μm molybdenum 1.96 keV 2.42 keV 2.25 keV 2.70 keV GeV { } { } --- { } --- { } 3.09 keV 3.50 keV 3.95 keV 4.47 keV GeV 1 { 1 } { } --- { } { } 3.95 keV 4.23 keV 4.77 keV 5.27 keV GeV --- { } { } --- { } { } We have been using an exponent value of 2.31 to model detector effects. - Relative integrated image area values for data and model are compared below. - The beam energies and filters provide comparison over a range of average x-ray energy. - The model has a finite number of x-ray energy bins but is being improved. E 2.31

Peterson xBSM Optics, Beam Size Calibration7 pinhole image relative integrated area (normalized to constant pinhole slit width) (normalized to particle beam current) {model} in red Jackson formula, with applied transmission: (E x-ray ) 2.25 data in black normalized no filter 4 μm diamond filter 2 μm molybdenum filter GeV { } { } { } GeV 1 { 1 } { } { } GeV --- { } { } { } E 2.25 A minimization of the differences between model and data yield a slight different exponent: E (x-ray) 2.25 The RMS difference between data and model is 15%.

Peterson xBSM Optics, Beam Size Calibration8 The EDGE provides more information about the x-ray photon energy distribution. By centering the x-ray beam on the “edge” of a rectangular opening in the gold mask on the optics chip, we measure the power through a silicon filter and a combination of gold and silicon filters. The transmission through the gold leads to the low (but not zero) pulse height region. The transmission is energy dependent. ( I do not compare these rates directly to the pinhole rates because there are different horizontal widths. ) But the ratio, PH low /PH high, is a value that can be compared to the model.

Peterson xBSM Optics, Beam Size Calibration9 R[Low/High] R[Low/High] R[Low/High] no filter diamond filter molybdenum filter R DATA R DATA R DATA DATA {model} / R model DATA {model} /R model DATA {model} /R model C-line GeV { } { } 1.10 { } C-line GeV { } { } 0.96 { } C-line GeV { } { 0.276} { } 0.80 D-line GeV { } review of LOW/HIGH values for EDGE key: { DATA } { model with (E x-ray ) 2.31 scaling, 4.0 μm diamond} E 2.31 Differences between model and data are minimized with an exponent: E (x-ray) 2.5, in some agreement with the results of the filter measurements. The RMS difference between data and model is again ~15%.

Peterson xBSM Optics, Beam Size Calibration10 Another test that can be performed is comparing the resultant image shapes with the data. Lines show image templates for various exponents, all with GeV, 4 micron diamond, (illustrated at 7 micron beam height). These are fit to the data.

Peterson xBSM Optics, Beam Size Calibration11 Three runs are used for the fit. Each has a corresponding pinhole run taken under the same bean conditions. The pinhole run is used to fix the beam size in the fit. The image shape suggests an exponent: ~ 2.8, but is “consistent” with (This the chisquared/dof, while the other results are RMS.) fits with Hybrid Template fitter Brian Heltsley

Peterson xBSM Optics, Beam Size Calibration12 Is the image template improved with the particular energy distribution? Or, is the image template sensitive only to the average energy? Lines show image templates for mono-energetic x-rays covering the range of the possible average energies.

Peterson xBSM Optics, Beam Size Calibration13 The fits to image template for various exponents, plotted as a function of the average energy. Also shown are the fits to mono-energetic x-rays. - The distribution of energies improves the fits. - Something interesting at 2.3 keV is due to rapidly changing phase shifts. fits with Hybrid Template fitter Brian Heltsley

Peterson xBSM Optics, Beam Size Calibration14 In summary, the model of an x-ray distribution: (Jackson 14.88) x E n is compared to the data in 3 ways: - transmission through filters affecting the pinhole image area - the relative transmission through the gold mask in the CA, - and the shape of the observed CA image. The three comparisons indicate that an exponent in the range { 2.2 : 2.8 } reasonably models the x-ray energy distribution.

Peterson xBSM Optics, Beam Size Calibration15 C: RD_ μm Au standard CA root=xr2m σ image = pixel σ beam =9.85 μm The modeled x-ray energy distribution results in an image template that can be used to fir CA data. Measurements agree with corresponding pinhole measurements.

Peterson xBSM Optics, Beam Size Calibration16 pinhole image relative integrated area (normalized to constant pinhole slit width, particle beam current) average x-ray energy in blue {model} in red Jackson formula, with applied transmission: (E x-ray ) 2.31 data in black no filter 4 μm diamond 7.2 μm aluminum 2 μm molybdenum particle energy 1.96 keV 2.42 keV 2.25 keV 2.70 keV GeV --- { } --- { } --- { } --- { } 3.09 keV 3.50 keV 3.95 keV 4.47 keV GeV 1 { 1 } 0.51 { } 0.14 { } { } 3.95 keV 4.23 keV 4.77 keV 5.27 keV GeV 1.82 { } 1.11 { } 0.31 { } 0.17 { } data/ E 2.31 December 2012, D-line preliminary

Peterson xBSM Optics, Beam Size Calibration17 The model can be used to predict the resolution power of the optics element. Shown: a coded aperture calculated image, smeared to beam sizes 5, 7 microns 16, 18 microns. Calculate the RMS difference of the smeared images.

Peterson xBSM Optics, Beam Size Calibration18

Peterson xBSM Optics, Beam Size Calibration19