A fast high spatial resolution optical t

Costanzo2 1 Department of Medical Physics, Royal Adelaide Hospital, Adelaide, Australia 2 School of Chemistry and Physics, University of Adelaide, Adelaide, Australia Abstract A fast tom

A fast, high spatial resolution optical tomographic

scanner for measurement of absorption in gel dosimetry

T van Doorn1,2, M Bhat1,2, T P Rutten2, T Tran2 and A Costanzo2

1 Department of Medical Physics, Royal Adelaide Hospital, Adelaide, Australia

2 School of Chemistry and Physics, University of Adelaide, Adelaide, Australia

Abstract

A fast tomographic optical density measurement system has been constructed and evaluated for application in Fricke

3D gel dosimetry Although the potential for full three-dimensional radiation dosimetry with Fricke gel dosimeters has

been extensively reported, its application has been limited due to a lack of fast optical density measurement systems In

this work, the emphasis of the design has been to achieve a short scan time through the use of precision optics and

minimal moving parts The system has been demonstrated in the laboratory to be able to achieve better than 1mm

resolution and a scanning time per tomographic slice of 2.4 seconds Full volumetric sampling of a 10 cm diameter by

7cm long cylinder can be achieved in 3 minutes When applied with a Fricke based gel dosimeter a linear response

between reconstructed CT number and absolute dose was better than 3%.

Key words gel dosimetry, optical CT, 3D dosimetry,

FBX dosimeter, conformal radiotherapy

Introduction

The need for reliable, three-dimensional dosimetry in

modern radiotherapy has been extensively reported in

conjunction with reports of developments in gel based

dosimetry1-21

Oldham et al.19 have proposed that the 3-D dosimetry

system should meet the RTAP(1,60,3,1) criteria (resolution

1×1×1 mm, imaging time 60 min, accuracy within 3%, and

precision within 1%) Oldham et al20 further described the

strength and limitations of different dosimeters using a

spider web plot A rating of zero indicates that a dosimeter

has no functionality for that specification; a rating of 5

indicates highest relative functionality An ideal dosimeter

with global application would rate 5 on all radial axes In

Figure 1, Oldham’s spider web plot has been extended to

include a tissue equivalence factor

Overall, gel dosimetry with optical scanners to measure

the induced attenuation is currently ranked the highest

Many optical gel scanning systems, including

commercial units, have been reported in the literature5-7,

9-12,14,17-23 Primarily they differ in the way the light

Corresponding author: Madhava Bhat, Department of Medical

Physics, Cancer Centre, Royal Adelaide Hospital, SA 5000,

Australia, Tel: 08-82222458, Fax: 08 82225937

Email: mbhat@mail.rah.sa.gov.au

Received: 22 April 2004; Accepted: 24 March 2005

Copyright © 2005 ACPSEM/EA

interrogates the sample A range of optical scanners developed by different groups are included in Table 1 While optical gel dosimetry has scored highly in Oldham’s spider plot for most parameters, it has ranked poorly for the time and cost factors There is also potential

to improve the accuracy and sensitivity

A fast optical CT scanning system is desirable to avoid degradation of the spatial dose information resulting from

Fe3 ion diffusion, thereby preserving quality and the integrity of imaged data Moreover, in a clinical setting a fast readout system has practical advantage over slow readout systems

In the work presented in this paper, a fast scanner based

on precision optics and minimal moving parts has been proposed to tighten the RTAP criteria to RTAP(1,3,3,1) (resolution 1×1×1 mm, imaging time 3 min, accuracy within 3%, and precision within 1%) Cost has also been proven to be able to be improved and the system is closer to Oldham’s optimal system It is appropriate to note however that the light attenuation through the gel is determined by changes in the optical absorption coefficient of the irradiated gels Whereas in irradiated polymer gels, the differential attenuation is the result of increased scatter24 The scanner is designed for absorption measurement in Fricke gels and has not been optimised for attenuation due

to scatter The reconstructed image by this scanner is therefore free from scatter artefacts highlighted by Oldham and Kim with highly scattering gels25

Materials - the optical scanner design criteria

The scanner was designed to have the capacity to form cubic voxels of 1.0 mm sides over a cylindrical sample

of 100 mm diameter and 70 mm length through the

0 1 2 3 4 5 Accuracy

Time

Energy

Resolution 3D

Cost

Sensitivity

Tissue Equivalence

Figure 1 Spider plot of important dosimetry specifications

common to all radiation therapies Radial axes correspond to the

different specifications and exhibit a scale from 0–5 The

performance of a dosimeter (or the requirements of a particular

treatment technique) is rated for each specification by a number

0–5, 0 = poor and 5 = high An ideal dosimeter would thus track

along the outside ‘‘5’’ spider track Adapted from M Oldham, et.

al., Med Phys., 2003, pp: 623-634.

Figure 2 Schematic diagram of scanner.

reconstruction of 1.0 mm tomographic slices orthogonal to

the axis of the cylinder at 1.0 mm intervals This volume is

adequate for typical SRS treatments and small field IMRT

Rapid projection scanning was implemented through

the incidence of a laser on a rotating mirror at the focal

point of a lens to create a parallel set of ray paths through a

rotating sample (see figure 2) Whenever the reflected beam

falls within the acceptance aperture of the first lens L1 the

beam is refracted parallel to the optical axis of the lens pair

(L1 and L2) (Rolyn Optics, model number 20.1328, 240

mm effective focal length) These lenses have both faces

anti-reflection coating for the visible spectrum

(400-700nm) with single layer magnesium fluoride, (MgF2) The

beam is then refracted by L2 to the ‘sample detector’

photodiode at the focal point of the second lens The laser

source and single photo-detector remain stationary

The HeNe laser (Coherent, Model Number 31-2772)

generated a 2mW CW beam of approximately 1 mm

diameter at 543.5 nm wavelength The laser generator

operates in TEM00 mode producing a low-divergence

RMS noise The narrow beam divergence of less than 0.99

m rad resulted in less than 1.8 mm increase in beam width over the optical path length of the system (~1.8 m) However, focussing lens L1 reduces the beam width to 0.1mm

Figure 3 is a photograph of the scanner with a sample gel in place The cylindrical gel sample was positioned in a refractive index matching bath10, midway between, and on the axis of, the twin lens pair The cylindrical sample housing provides for rotationally invariant sampling during the tomographic scanning process The bath measured 14.0 (W) ×14 (L)× 10 (H) cm and the transparent wall facing the laser beam was constructed of optical quality glass to minimize refraction The diameter of the gel cylinder was made larger (120 mm) than the target diameter (100 mm) to reduce refraction effects on laser beam near the edges of target cylinder (see Figure 2)

The current through the photodiode detector with time was in proportion to the optical attenuation of the beam as it was swept across a path that is displaced from, but constantly parallel to, the optical axis of the lens pair For calibration purposes, a stationary mirror momentarily reflected the laser beam, un-attenuated by gel the sample, onto the sample detector, providing a reference signal for correction of laser beam intensity fluctuations This reflected beam is attenuated so that a reference signal is approximately equal to the sample signal

Sampling volume and rate

The cylindrical sample holder was mounted on a belt driven platform inside the refractive index matching bath, for rotation through known angular increments (1.25 degrees) With maximum mirror rotation speed of 120 revolutions per second, a 180° sinogram can be achieved in 2.4 seconds and the whole volume swept in approximately

3 minutes (70 x 2.4 seconds) Rigid mounting of the rotation platform with respect to the optical axis of the twin lens system ensured correct alignment of the two centres of rotation for accurate CT reconstruction

The relationship between sweep rate, projection width and sampling rate is illustrated withthe helpof figure 4a The number of samples required per sweep period determines the sampling rate The sweep period (S) is the product of the period of rotation of the mirror (T) and the arc of circle (C) subtended by the projection width (P) and the focal length (f):

T C

where

π









×

=

−

f

P

tan

(2) With the component dimensions defined above and 500 samples per projection, each sample must be acquired in less than 1 microsecond

The scanning process is a translation of a rotational motion to a displacement off axis whichis non-linear with time The angle subtended by the rotating mirror θs in the

Figure 3 Photograph of optical CT scanner The laser beam sweeps across the gel in

parallel lines and a projection of the gel matrix is recorded by the detector.

(a)

(b)

Figure 4 a) Relationship of sweep rate, projection width and sampling rate b) Lateral

Displacement (w) of laser beam during sampling interval.

Laser

Rotating mirror Lens 1

Sample

Lens 2

Detector Water bath

Detector

θs θb

θa

w p

f

Table 1.

Appleby A and

Leghrouz A.5 1991 Demonstrated visualisation of radiation dose distributions by naked eye using gel

sections

Tarte B.J and van

Doorn T.6,7 1993 Linear optical tomographic scanning of ferrous sulphate gels for full three dimensional

imaging of dose

Gore et al10 1996 Optical CT scanner for polymer gel sample in a fixed phantom and translating mirrors

for optical transmission data acquisition Transmission data required correction to account for deviation of laser beam from its normal incidence angle Total data acquisition time for a 60x60 pixel image was 6 min

Tarte et al11 1997 Demonstrated linear optical response up to 10 Gy dose in laser scanned agarose gel

sections Relative dose distributions in good agreement with ionisation chamber readings

Kelly et al12 1998 Optical CT scanner resembling a “first generation” x-ray CT scanner developed with

fixed beam and rotating FBX gel sample in a translating phantom for optical transmission data acquisition Transmission data required correction to account for deviation of laser beam from its normal incidence angle Data collection time per slice for 100x100 pixels was 1 h

Wolodzko et al14 1999 CCD camera based detector, manual rotation of the FBX gel phantom to acquire CT

projection data Highlighted that non uniform pixel sensitivity is an issue to be resolved in CCD based optical CT reconstruction

Oldham et al19 2001 Compared MR scanned image with laser scanned optical CT image of polymer gel

Defined Resolution Time-Accuracy-Precision (RTAP) criteria.(resolution <1 mm3, time <1h, accurate within <3%, precision <1%) Found optical CT scanner was able to meet the RTAP criteria but MR scanner failed to meet the criterion on resolution Doran et al21 2001 Introduced a method to correct non-uniform pixel sensitivity in the reconstructed CT

image Optical simulation was used to correct the intensity of the projection data to take into account of reflection and refraction Image reconstruction time was under a minute

Wuu et al22 2003 Application of optical CT reconstruction in calculating 3D dose image of Re-188

liquid balloon for intravascular brachytherapy using a single laser in rotation translation type optical CT scanner with polymer gel and a large photo-detector (1 cm x1cm)

Oldham et al21 2003 Proposed spider pot to specify requirements of dosimetry system across the spectrum

of clinical treatments and demonstrated that their prototype optical CT scanner met the RTAP criteria

Islam et al17 2003 Performance evaluation of a commercial optical CT scanner (Octopus laser CT

scanner, MGS Research Inc, a rotate- translate optical scanner) and polymer gel Authors found discrepancy in gel measured dose and film measured dose of about 17% and corrected it using a normalisation factor Under test condition, scanning time per slice was of the order of 600 seconds

Xu et al23 2004 Performance evaluation of commercial optical CT scanner (Octopus laser CT scanner,

MGS Research Inc) and polymer gel and compared 3D dose distribution results with film dosimetry results The 3D dosimeter demonstrated the ability to reproduce dose distribution with 3% uncertainty However, authors have not dealt with the time required to complete the scanning process

Figure 5 Circuit diagram of detecting diode and pre-amplifier.

°

×

×

where θ a and θ b are shown in figure 4B and r is

T1 the rotation rate of the mirror

But











 +

f

w p

b tan1

and









f

p

a tan1

where f is the focal length of a lens, p is the position of the

beam off-axis at the start of the sampling interval and p+w

at the end of the sampling interval









−







 +

=

f

p f

w p

re-arranging for w,

p f

p rt

f

w= tan360 s+tan−1 − (7)

Refractive index matching

The refractive indices of the water bath, gel container

and gel were matched to provide a sampling region of

constant refractive index Matching the refractive indices

also reduced the noise in the detected signal from light

scattering from imperfections in the gel container

The refractive index of the gel was measured with an

Abbé Refractometer (Hilger & Watts 1948) to be

1.338±0.001 Since the refractive index of the gel cannot

easily be changed without altering the tissue equivalence of

the gel, the refractive index of the gel container and water

bath were matched to the gel The refractive index of water

(~1.3326 @ 24oC for white light) can be increased by

adding glycerol (Aldrich #13,487-2); refractive index

of 1.4722 @ 24oC) For low glycerol concentrations, every 2 mL of glycerol added to 250 mL of water raised the refractive index of the water by 0.001 The absorbance of a 20% glycerol solution was measured (using a spectrophotometer (referenced to pure water) and found to produce a negligible change in light absorption

To minimize refraction, the gel container was constructed from Fluorinated Ethylene Propylene (FEP) with n = 1.338 The FEP tube had a diameterof 12 cm and wall thickness of 0.3 mm (manufactured by ADTECH polymer Engineering LTD, UK)

Detector circuit.

The detector (UDT PIN13D high responsivity PIN photodiode) had an active surface area of 13 mm2, and responsivity at 543.5 nm of 0.26 A/W The typical 14 ns rise time at 632 nm with a 50-ohm load resistor and with a negative bias of 10 V [UDT Sensors catalogue] was nearly three orders of magnitude less than the derived minimum sampling time

A reverse biased photoconductive (figure 5), rather than photovoltaic configuration, resulted in shorter rise times and improved linearity of current response The generated photocurrent was proportional to the incident light power and was converted to a voltage using a transimpedance amplifier configuration The gain-bandwidth product and noise performance of CLC 425 operational amplifier was in excess of the response requirements in this configuration Extraneous noise pick

up was minimised through short leads between the photodiode and pre-amplifier inputs

Data capture and manipulation

The detecting amplifier output against time was captured with an Acqiris single channel DP110 PCI Digitiser Card with Oscilloscope Characteristics The digitiser had a 250 MHz bandwidth, 8 bit resolution, with sampling rate of 1 GS/s The captured data was manipulated in MATLAB version 7.0 (The MathWorks, Inc) with an image processing toolbox to form a single sinogram matrix (0° to 180°, in 1.25° increments, 500 samples per projection) This matrix was inverse Radon transformed using an inbuilt function available in MATLAB which included options for filtering by a ramp, Shepp-Logan26, or sine filter to reduce aliasing and either nearest neighbour or linear interpolation

Method - scanner performance evaluation

Alignment

Alignment of the system was achieved when the most constant (within noise constraints) signal output was measured as the laser beam was swept at normal incidence across the front surface of the gel tank filled with distilled water

Figure 6 Measuring the spot size of a laser using a knife-edge to block part of the beam.

Figure 7 Signal rise distance for the standard laser beam and an additionally focussed laser beam

as they were swept across a knife-edge.

Spatial performance

The spatial performance of the scanner was assessed

through measurement of the detector response time and

the width of the laser beam A knife-edge technique

was used to measure the width of the laser beam27

The inherent beam width of the laser was measured to

have a waist of 0.515 mm located 554 mm behind the

laser face The width of the laser beam in the sample

was measured experimentally using a knife-edge placed

at the midpoint of the matching tank The knife-edge

was mounted on a translation stage micrometer and

moved through the beam (Figure 6) The position of the

knife edge and the respective photodiode output were

recorded This edge response was then differentiated to give

the line response function and the FWHM measured to

determine the laser beam width at the axial position of the

knife-edge

The detector response time and the time constant of the

pre-amplifier were demonstrated by measuring the signal

rise distance for the standard laser beam and an additionally

focussed laser beam (Figure 7) as they were swept across a

knife edge With the tank centred on the beam’s waist, the

rise times were recorded for the knife-edge located at the centre of the tank

Photodiode linearity

The linearity of the UDT PIN13D diode was determined by measuring the change in output signal as a result of a change in the incident light power Neutral density filters were used to modulate the intensity of incident light and the output signal was recorded from the ADC card

Gel dosimeter linearity

A freshly prepared batch of gel dosimeter containing 0.1 mM Fe++, 0.05 mM xelenol orange, 0.5 mM benzoic acid, 25 mM H2SO4 and 4% gelatin was placed in a number

of 1 cm path length cuvettes The concentrations of gel ingredients dependent on radiation sensitivity and dose ranges involved in the clinical set-up24 The linearity of the gel dosimeter was determined by measuring the change in the optical density for a range of doses delivered to these cuvettes using a spectrophotometer Optical density was measured at 543.5 nm wavelength light

Detector

Gaussian laser beam

Knife-edge

Rise Distance

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Distance (micrometre)

focussed beam normal beam

Figure 8 Linearity of the photo diode determined by measuring

the change in output signal as a result of a change in the incident

light power.

Figure 9 The linearity of the gel dosimeter was determined by

measuring the change in the optical density for a range of doses

delivered to 1 cm path length cuvettes using a spectrophotometer.

Figure 10 Sinogram of the data captured (from 0° to 180°,

in 1.25° increments, 500 samples per projection) after

irradiating the gel with 4 circular 13 mm diameter fields of

2.5, 2.0, 1.5, 1.0 Gy respectively.

Gel dosimeter linearity from reconstructed image.

A freshly prepared batch of gel dosimeter containing

0.1 mM Fe++ as above was placed inside the FEP gel

container and then irradiated with 4 circular 13 mm

diameter fields of 2.5, 2.0, 1.5, 1.0 Gy using a 4 MV x-ray

beam at 100 cm SSD respectively Thirty minutes post

irradiation time was allowed for the gel to complete chemical change The gel was then optically scanned at a depth of 1 cm and back projection was applied with nearest neighbour interpolation The captured data (0° to 180°, in 1.25° increments, 500 samples per projection) is shown in a single sinogram matrix (Figure 10) A Shepp-Logan filter was also applied during reconstruction to reduce the noise

in the final image The average over 25 pixel values in the central areas of each dose region of the optical-CT-reconstructed image was then recorded

A similar method was also used to expose a separate gel mix to a 17 mm circular field at 100 cm source to surface distance The centre of the circular field was blocked using a 10 mm diameter circular shielding block to produce a ring pattern in the gel This was repeated five times in order to produce an Olympic ring pattern A radiation dose of 1.5 Gy was delivered for each ring

Results and discussion

Alignment and active area of the detecting diode

With accurate alignment of the system, the signal output was constant With the detector correctly centred in the beam, slight angular adjustment of the photodiode produced only a negligible change in output signal Smaller detectors were found to have the disadvantage of being highly sensitive to small changes in the position of the detector normal to the optical axis and refraction of light causing light not to be collected by the diode

Spatial resolution

The spatial resolution of a tomographic system is dependent on a combination of factors relating to the configuration For the current configuration these factors include the sampling rate, the laser beam width, the detector response time and Fe3 ion diffusion The overall limit of performance, or sink point, will be determined by the poorest of these four factors

Many authors have extensively studied ion diffusion in Fricke gel dosimeter that impacts upon spatial dose information24,28-32 This problem has been minimised by the use of xylenol orange as a chelating agent that significantly decreases diffusion24 Further, the effect of ion diffusion on spatial resolution is minimised by a fast scanning system, allowing no time for the diffusion process during the scanning procedure Thus, the overall effect of ion diffusion

on spatial dose information is less important in comparison

to other factors that are discussed in this section

The sampling rate was set at one per microsecond which corresponded to a lateral sweep (w in equation 7) of 0.226 mm at the centre of the projection At the periphery

of the projection this increased by approximately 3% to 0.232 mm Ideally, the laser beam width should be of the same order as twice the sampling width (Nyquist sampling theorem) as it passes through the gel sample The addition

of a specifically designed focusing system in the laser path can be used to modify the beam width (see Appendix and Figure A1) Strong focusing can produce a very narrow

Absorbed dose vs optical density

0

0.2

0.4

0.6

0.8

Absorbed Dose (Gy)

Linearity of photodetector response

0.1

1

10

Optical Density

Figure 11 Reconstructed image of one slice of a gel irradiated

with 4 circular 13 mm diameter fields of 2.5, 2.0, 1.5, 1.0 Gy

respectively.

Figure 12 The average over 25 pixel (representing 1 mm 2 ) values

in the central areas of each dose region shown in figure 11 plotted

against dose demonstrate a non-linearity of better than ±3% up to

2.5 Gy.

waist in the centre of the tank (line (a) figure A1) but will

result in rapid divergence of the beam Lesser focusing

decreases the divergence (line (b) figure A1) but also

enlarges the beam width In practice, the inherent focusing

of lens L1 produces a beam that has the minimum width at

the edges of the sampling volume (line (c) figure A1)

The knife edge measurements at the middle of the

sampling volumes gave a FWHM value of 0.1 mm which

was in good agreement with the theoretically determined

focused value The rise time of the detecting circuit (10 %

to 90%) (converted to spatial equivalent) also demonstrated

good agreement with the narrow laser waist measured to be

50 µm while the inherent focusing of a normal laser beam

passing through lens was 100 µm

The sink point in the resolution chain for this system

was therefore the sampling rate However, the RTAP

criterion of 1mm was readily met

Linearity of response

The photodiode preamplifier output versus optical

density from zero to one is shown in Figure 8 The

non-linearity over this range was less than ±2% The change in

the optical density of the gel versus dose delivered for a 0

to 6 Gy dose range is shown in Figure 9 The linearity of the gel dosimeter optical density was better than ±2% over this range Linearity of Fricke gel dosimeter has been reported up to 20 Gy2,6,12,24 Tomographically reconstructed regions of known dose are shown in Figure 11 Using the matlab code the pixel values of reconstructed image were normalised to give zero pixel value for zero dose The reconstructed pixel values plotted against dose, demonstrate

a non-linearity of better than ±3% up to 2.5 Gy dose (Figure 12) Repeated dose measurement from the reconstructed image from a fresh batch of gel dosimeter show that reproducibility is better than 1%

Although the results presented here are for doses up to 2.5 Gy the range of the linear response could be extended easily by changing chemical composition of Fricke dosimeter The photodiode used in this study has a linear response with the incident light power A non- linearity

of less than ±1% over 6 decades is specified for planar diffused photodiodes Hence, these detectors can be used for a wide range of dose measurements

Tomographic image reconstruction

The reconstructed image of the Olympic ring exposure pattern is shown in Figure13a with a pixel value profile

Figure 13 Reconstructed image of one slice of a gel irradiated to

produce an Olympic ring pattern (Figure 13 a) and pixel value profile across the image indicated by the line (Figure 13 b) A circular field of 17 mm diameter at 100 cm source to surface distance was shielded using a 10 mm diameter circular block to produce a ring pattern in the gel This was repeated five times in order to produce an Olympic ring pattern.

Dose vs Pixel value of reconstructed image

R 2 = 0.9986

0

0.5

1

1.5

2

2.5

3

Dose (Gy)

a

b

D Cq

B Aq q

i

i

+

=

across the pattern shown in Figure 13b This shows

multiple overlapping fields are reconstructed accurately

Creation of such standard image patterns and comparing

them with the baseline data becomes an important quality

assurance tool for the optical CT scanning system

To produce the best image quality, care needs to be

taken in the whole process of 3D gel dosimetry: from gel

preparation, storage, irradiation and to data acquisition

Image quality is significantly reduced when insufficient

samples are collected Very tiny suspended particles can

also degrade image quality Accurate centre of rotation is

crucial to avoid artefacts and contour distortion Missing

data will produce streak artefacts and signal noise can

significantly reduce contrast resolution

While most aspects of gel dosimetry have been

extensively reported in the literature, the work presented

here has demonstrated the feasibility of a fast optical

scanner with a single slice data set being acquired in 2.4

seconds The relative simplicity of the design makes the

system robust, easily aligned and the minimal number of

moving parts encourages long term reliability A further

benefit of this optical scanner is its relative low cost

compared to other types of gel dosimetry scanners and

comparative cost to existing optical scanners

Conclusion

The design and construction of an optical absorption

CT scanner with the potential to satisfy the RTAP(1,3,3,1)

criteria has been demonstrated Primarily the scanner has a

use in Fricke gel dosimetry and has been shown to have a

linear response up to 2.5 Gy The short imaging time has

the potential to make Fricke gel dosimetry an attractive

proposition for routine clinical use However, before the

system is introduced into the clinic, the characteristics of

the optical CT scanner in relation to its accuracy,

reproducibility, spatial distortion, energy response and

sensitivity to radiation must be studied in greater detail

This work is under way and the results will be reported in

the near future

Appendix

The correct size of laser waist depends on the tank

width and the refractive index of the medium inside the

tank

ABCD matrices can be used to relate the input and

output characteristics of a beam passing through an optical

system27

Using the paraxial approximation,

























=













1 1 0

0

α

Y D C

B A

α

Y (8)

Where Y0 and Y1 are the ray’s initial and final height, α 0

and α1 are the ray’s initial and final slope It can be shown

that ABCD matrices can also be used to relate the input and output complex radius of curvature of a Gaussian spherical wave passing through an optical system through the relation

(9)

where qi and qf are the input and output complex radii of

curvature Equation 9 known as the ABCD propagation law

So, if we know the initial complex radius of curvature,

qi of a TEM00 laser beam, then pass it through a complicated optical system represented by the matrix













D C

B

A we can simply calculate the final complex radius

of curvature qf using Eqn.9

A Mathematica program was written to find the

optimum waist spot size It finds the value of ωo, which

minimises the spot size at the edges of a tank of n = 1.338, assuming laser light of wavelength 543.5nm (in air) It is important to specify the refractive index of the medium inside the tank because this will alter the wavelength (λ) of the light passing through it according to the relation

n

c λ

f = (10)

where f is the frequency and c is the speed of light.

Changing the wavelength changes the spot size of the beam

as a function of z through Eqn (9)

Acknowledgement

The authors would like to acknowledge the contributions made in the manufacturing of this device by Andrew Frolov, Shane Hein, David Horsman and Ann Tran, the staff of Radiation Engineering, Department of Medical Physics, RAH Without their contributions the progress reported in this paper would not have been able to

be achieved

Figure A1 Beam shapes (

2

1

e intensity lines) for different degrees

of focusing of the laser inside a tank of half width 70mm The best beam has the smallest spot size at the edge of the tank.

0.05 0.1 0.15 0.2 0.25

z (mm)

ωo (mm)

a b c

The output of the program gives the optimum waist

spot size (the one that minimises the spot sizes at the tank

edges) for a range of tank widths It was found that for the

current tank half width of 70.5 mm, the ideal waist spot size

is 0.09548 mm, which expands to 0.13 mm at the tank’s

edge It could be reasonably assumed that beam’s full width

at half maximum at the tanks edge to be the spatial

resolution, and hence the best spatial resolution achievable

for a tank of half width 70.5 mm (and n=1.338) is 0.15 mm

References.

1 Gore, J C., Kang Y S., Measurement of radiation dose

distributions by nuclear magnetic resonance (NMR) imaging,

Phys Med Biol., 29:1189-1197, 1984.

2 Appleby, A., Christman, E A., Leghrouz, A., Imaging of

spatial radiation dose distribution in agarose gels using

magnetic resonance, Med Phys., 14:382-384, 1987.

3 Olsson, L E., Petersson, S., Ahlgren, L., Mattsson, S.,

Ferrous sulphate gels for determination of absorbed dose

distributions using MRI technique: basic studies, Phys Med.

Biol., 34:43-52, 1989.

4 Hazle, J D., Hefner, L., Nyerick, C E., Wilson, L., Boyer, A.

L., Dose-response characteristics of a ferrous-sulphate-doped

gelatin system for determining radiation absorbed dose

distributions by magnetic resonance imaging (Fe MRI), Phys.

Med Biol., 36:1117-1125, 1991.

5 Appleby, A., Leghrouz, A., Imaging of radiation dose by

visible colour development in ferrous-agarose-xylenol orange

gels, Med Phys., 18:309-312, 1991.

6 Tarte, B J., van Doorn, T., Absorbance measurement with a

Helium-Neon laser for chemical dosimetry, Aust Phys &

Eng Sc Med., 16:75-78, 1993.

7 Tarte, B J., van Doorn, T., Optical scanning of Ferrous

Sulphate Gels for Radiotherapy Treatment Dosimetry,

Australasian Conference on Physical Science and Engineering

in Medicine and the Biomedical Engineering Conference 1993

Proceedings, pp126, 1993.

8 Kron, T., Pope, J M., Dose distribution measurements in

superficial x-ray beams using NMR dosimetry Phys Med.

Biol., 39:1337, 1994.

9 Tarte, B J., van Doorn, T., Laser-based tomographic scanning

of gel volumes for applications in ionising radiation

dosimetry, Tenth Conference of the Australian Optical

Society, Brisbane, 1995.

10 Gore, J C., Ranade, M., Maryanski, M J., Schulz, R J.,

Radiation dose distributions in three dimensions from

tomographic optical density scanning of polymer gels: I

Development of an optical scanner, Phys Med Biol.,

41:2695-2704, 1996.

11 Tarte, B J., Jardine, P A., van Doorn, T., Development of a

CCD array imaging system for measurement of dose

distributions in doped agarose gels, Med Phys.,

24:1521-1525, 1997.

12 Kelly, R G., Jordan, K J., Battistaa, J J., Optical CT

reconstruction of 3D dose distributions using the

ferrous-benzoic- xylenol (FBX) gel dosimeter, Med Phys.,

25:1741-1750, 1998.

13 De Deene, Y., et al., Three-dimensional dosimetry using

polymer gel and magnetic resonance imaging applied to the

verification of conformal radiation therapy in head and-neck

cancer, Radioth Onc., 48:283–291, 1998.

14 Wolodzko, J G., Marsden, C., Appleby, A., CCD Imaging for

Optical Tomography of Gel Radiation Dosimeters, Med.

15 Mcjury, M., Oldham, M., Cosgrove, V P., Murphy, P S.,

Doran, S., Leach, M O., Webb S., Radiation dosimetry using polymer gels: methods and applications, Brit J Radiology,

73:919-929, 2000.

16 De Deene, Y., De Wagter, C., Van Duyse, B., Derycke, S., Mersseman, B., De Gersem, W., Voet, T., Achten, E., De

Neve, W., Validation of MR-Based Polymer Gel Dosimetry as

a Preclinical Three-Dimensional Verification Tool in Conformal Radiotherapy, Magnetic Resonance in Medicine,

43:116–125, 2000.

17 Islam, K T S., Dempsey, J F., Ranade, M K., Maryanski, M.

J., Low, D A., Initial evaluation of commercial optical CT-based 3D gel dosimeter, Med Phys., 30:2159-2168, 2003.

18 Doran, S J., Koerkamp, K K., Bero, M A., Jenneson, P.,

Morton, E J., Gilboy, W B., A CCD-based optical CT scanner for high-resolution 3D imaging of radiation dose distributions: equipmen specifications, optical simulations and preliminary results Phys Med Biol., 46:3191–3213, 2001.

19 Oldham, M., Siewerdsen, J H., Shetty, A., and Jaffray, D A.,

High resolution gel-dosimetry by optical-CT and MR scanning, Med Phys 28:1436-1445, 2001.

20 Oldham, M., Siewerdsen, J H., Kumar, S., Wong, J., Jaffray,

D A., Optical-CT gel-dosimetry I: Basic investigations, Med.

Phys., 30:623-634, 2003.

21 Doran, S J., Koerkamp, K K., Bero, M A., Jenneson, P.,

Morton, E J., Gilboy, W B., A CCD-based optical CT scanner for high-resolution 3D imaging of radiation dose distributions: equipment specifications, optical simulations and preliminary results, Phys Med Biol., 46:3191-3213,

2001.

22 Wuu, C S., Schiff, P., Maryanski, M J., Liu, T., Borzillary,

S., Weinberger, J., Dosimetry study of Re-188 liquid balloon for intravascular brachytherapy using polymer gel dosimeters and laser-beam optical CT scanner, Med Phys., 30:132-137,

2003.

23 Xu, Y., Wuu, C S., Maryanski, M J.,Determining optimal gel sensitivity in optical CT scanning of gel dosimeters, Med.

Phys., 30:2257-2263, 2003.

24 Schreiner, L J., Review of Fricke gel dosimeters, Third International Conference on Radiotherapy Gel Dosimetry,

Journal of Physics: Conference Series 3:9–21, 2004.

25 Oldham, M., Kim, L., Optical-CT gel-dosimetry II: Optical artefacts and geometrical distortion, Med Phys.,

31:1093-1104, 2004:

26 Shepp, L A., Logan, B F., The Fourier reconstruction of a head section, IEEE Tr Nuc Sci., 21:21-43, 1974.

27 Siegmann, E., Lasers, University Science Books, California

USA, 1986.

28 Baldock, C., Harris, P J., Piercy, A R., Healy, B.,

Experimental determination of the diffusion coefficient in two dimensions in ferrous sulphate gels using the finite element method, Aust Phys & Eng Sc Med., 24:19-30, 2001.

29 Harris, P J., Piercy, A., Baldock, C., A method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements, Phys Med Biol.,

41:1745-1753, 1996.

30 Chu, K C., Jordan, K J., Battista, J J., Van Dyk, J., Rutt, B.

K., Polyvinyl alcohol-Fricke hydrogel and cryogel: two new gel dosimetry systems with low Fe3+ diffusion, Phys Med.

Biol., 45:955-969, 2000.

31 Schreiner, L J., Audet, C., Eds., DOSGEL 1999, Proc 1st Int.

workshop on Radiation Therapy Gel Dosimetry, Canadian Organization of Medical Physicists, Edmonton, 1999.

32 Baldock, C., De Deene, Y., Eds., DOSGEL, 2001, Proc 2nd

Int Conf Radiotherapy Gel Dosimetry, Queensland