# Presentation: 190598

## X-RAY IMAGING PRACTICUM

- Brian Dennis, GSFC
- Gordon Hurford, UCB

## X-RAY IMAGING PRACTICUM

- Objectives
- Intuitive perspective on RMC imaging
- Introduction to some real-world hardware and design considerations
- Introduction to how visibilities are related to modulation patterns and how they can be used

## Slide 3

## Slide 4

## Slide 5

## Slide 6

## Mounts for Grids 1 - 4

## Grid #4 Kinematic Mounts

## Coarse Grids #5 - 9

## Stacking Coarser Grids

## Optical CharacterizationFacility

## Grid #2Pitch 59 mm Slit width 41 mmThickness 2.04 mmMaterial Tungsten

## OGCFResults

## X-RayGridCharacterizationFacility

- X-RayGridCharacterizationFacility

| Source | Energy (keV) | Strength on 5/19/1998(mCi) |
| --- | --- | --- |
| Cd109 | 22 | 50 |
| Co57 | 122129 | 40 |
| Cs137 | 662 | 40 |

- Radioactive Sources Used

## Grid #4 X-ray Angular Response

## Grid #4 transmission as a function of angle to normal & energy.

- + Cd109
- Co57
- X Cs137

##  Definition of model fit parameters used to characterize the angular dependence of the grid transmission. 

-  Definition of model fit parameters used to characterize the angular dependence of the grid transmission.

## Factors that degrade modulation

Grid transparency
Difference in grid pitch
Relative twist
Aspect errors
Random errors in slit / slat locations
Diffraction

Need to limit effective sum of errors to achieve satisfactory modulation efficiency

- Grid transparency
- Difference in grid pitch
- Relative twist
- Aspect errors
- Random errors in slit / slat locations
- Diffraction
- Need to limit effective sum of errors to achieve satisfactory modulation efficiency

## Combining errors

- Key to RHESSI error budget was that each error source was equivalent to ‘smearing’ the source in a distinctive way
- Fixed source + aspect error = perfect aspect + moving source
- Fixed source + twisted grids =  perfect grids + distributed source
- Use ‘gaussian model’ of smeared source to calculate loss of modulation

## Numerical example

- Grid 1:  35 microns, 1.55m, 7cm diameter
- Twist of 35microns/7cm smears source over 1 modulation cycle  zero modulation.
- Compare twist tolerance to angular resolution!

## Exercise 1

- Consider RHESSI grid 1:
-  34 micron pitch
-  25 micron apertures
- 1 mm thick
-  separated by 1.55m
- Grids 9 cm in diameter
- Detector 6 cm in diameter
- What is the FWHM resolution of RMC1 (assume 1st harmonic only) ?
- How much relative twist is required to totally destroy the modulation?
- What would be the qualitative and quantitative effect of a relative twist of 1⁄2 of this amount ?

## Slide 22

- Spin axis at  [246,-73 ]
- Grid 8 slits were pointed at solar north at 18:58:08.5 UT and rotating at 15 rpm (clockwise looking at rear of collimator)
- What is the source location?
- Bonus questions:    What is effect of a 1 arcminute error in the pointing?
- 		a 1 arcminute error in the aspect solution?
- 		a 1 acminute error in the roll aspect?
- Do a back projection image grid 8, 28-aug-2002 185750-185850 and compare to your estimate.   Alternatively, use his_vis_fwdfit on the visibilities.

- Exercise 2

## Slit/Pitch Ratio & Modulation Efficiency

## What are Visibilities?

-   A visibility is the calibrated measurement of a single Fourier component of the source image.

- V(u,v) =  ∫∫ I(x,y) e-2i(ux+vy) dx dy

- V – visibility
- u, v – inverse period in x, y
- period = 2 x FWHM
- l – count rate (count s-1)

## Role of Visibilities

- Time-modulated RMC light curve    (=eventlist)

- Set of measured visibilities

- Image

-   Visibilities represent an intermediate step between 	modulated signal and image.

- Current imaging algorithms

- Little loss of information

- Fourier transform

- Calibrated & compact

## Single Visibility Measurement

- Visibility for one RMC at one orientation is determined
- by calibrated amplitude (A) and phase (Φ) )of modulation

- V(u,v) = A e iΦ

- u, v define spatial frequency at which the visibility is measured
**√**( u**2** + v**2** ) =  0.5 / (FWHM resolution)            TAN (orientation) = v / u

- A visibility measures one Fourier component of source image.

- USEFUL PROPERTY:  Unmodulated background is ignored.

- Typical modulated light curve

## Single  Visibility Properties 

- Image                       Visibility

- For single sources:
-   Amplitude depends on flux 	and size
-   Phase depends on position
- For multicomponent sources:
- Visibilities add vectorally

- Φ

- A

## Image            Visibilities

- x,y
- u,v

## Image            Visibilities

- x,y
- u,v

## Image            Visibilities

- x,y
- u,v

## Image            Visibilities

- x,y
- u,v

## Image            Visibilities

- x,y
- u,v

## Image            Visibilities

- x,y
- u,v
- rhessiu,v

## Measuring Visibilities with RHESSI

- Map calibrated eventlist to roll/phase bins with stacker.       	(This is the only time-consuming step.)
- For each roll bin, fit count rate vs. phase.
- Save measured visibilities as a “bag of visibilities”.
- Optionally display / edit / combine visibilities.
- Use visibilities in your application.

## Mapping Time Bins to Roll/Phase Bins

## Roll and Phase Bins

## Rate vs. Phase Bin Fits

- Typical plots of rate vs. phase bin at 8 roll orientations.

- 5 parameter fits of amplitude and phase at fundamental and 2nd harmonic

- USEFUL PROPERTY:
- Evaluates statistical errors in visibilities.

## Displaying Visibilities

- Amplitude and phase vs. position angle
- RMC 7                                         RMC 6

- USEFUL PROPERTIES:
- Amplitudes and phases are fully calibrated (ph/cm2/s).
- Phase coherence is a reliable indicator of ‘detection’.
- Conjugate visibilities can be averaged.

##  Visibility Applications

-   hsi_vis_fwdfit determines the best fit parameters for simple sources
- 	Flux, size, orientation, location vs. time, energy
- 	Ability to fit albedo
-   mem_njit = a new, visibility-based maximum entropy algorithm
-   Insight into imaging performance and limitations
-   Improved grid calibration
-   Harmonics
-   Can be used as input to radio astronomy imaging packages
-   Imaging in photon energies, not detected energies
-   High time resolution studies
-   Long time integrations
-   Weighting (t, E) may enhance sensitivity for weak sources
-   Source fine structure

## hsi_vis_fwdfit

-   Visibility-based imaging algorithm that determines best-fit 	parameters for simple source geometries
-   Currently supported shapes
-   Elliptical gaussian (default)
-   Circular gaussian
-   Loop ( = curved elliptical gaussian)
-   Two circular gaussians
-   An optional, combined albedo component
- User selects shape and approximate location
-   Determines statistical errors in fitted parameters

- ASSUMES selected shape is a good representation of real source !!!

##  Visibility Software

- Example:
- To make a set of visibilities,
- 	vis = his_vis_usershell (time=‘2005-jul-30 ‘+[’06:29’, ’06:36’], $                    			energy=[25,50],	xyoffset=[-810,140],             $				phz_radius=30)
- To display visibilities:			optional
- 	hsi_vis_display, vis, /ps
- To make a forward fit map (assuming a curved  elliptical gaussian)
- 	his_vis_fwdfit, vis, /loop, /showmap

- Preliminary version of visibility software is on ssw

- For details:
- sprg.ssl.berkeley.edu/~ghurford/VisibilityGuide.pdf

## Demo of hsi_fwd_fitand exercise with Aug 28 event