- Email: [email protected]
Measurement of sensitivities for the thermal recording of laser beams
Measurement of sensitivities for the thermal recording of laser beams C.R. PRASAD, K.A. NIRMALA, PRABHA VENKATESH
A simple technique for determining the energy sensitivities for the thermographic recording of laser beams is described. The principle behind this technique is that, if a laser beam with a known spatial distribution such as a Gaussian profile is used for imaging, the radius of the thermal image formed depends uniquely on the intensity of the impinging beam. Thus by measuring the radii of the images produced for different incident beam intensities the minimum intensity necessary (that is, the threshold) for thermographic imaging is found. The diameter of the laser beam can also be found from this measurement. A simple analysis based on the temperature distribution in the laser heated material shows that there is an inverse square root dependence on pulse duration or period of exposure for the energy fluence of the laser beam required, both for the threshold and the subsequent increase in the size of the recording. It has also been shown that except for low intensity, long duration exposure on very low conductivity materials, heat losses are not very significant. KEYVVORDS: lasers, thermographic recording, carbon photographic paper
Introduction The t h e r m a l r e c o r d i n g of laser b e a m s is utilized in m a n y applications, for example, in recording i n l b r m a t i o n on optical storage discs that have surfaces specially p r e p a r e d ibr u r i t i n g with m o d u l a t e d laser beams, a n d lor visualizing the b c a m s h a p e of infra-red lasers like N d : Y A G ( 1.06/xm) or C O 2 (10.6/,tin) on t h e r m a l l y sensitive m a t e r i a l s such as c a r b o n sheets or d e v c l o p e d p h o t o g r a p h i c papers. T h e latter a p p l i c a t i o n is a very' c o n v e n i e n t a n d inexpensive alternative to the c o n v e n t i o n a l m e t h o d of using infra-red sensitivc or sensitized' p a n c h r o m a t i c films, infra-red p h o s p h o r s , p h o t o d e t e c t o r ( s i l i c o n or pyroelectric) arrays or infrared vidicon cameras, etc, that arc expensive a n d often difficult to u s e T h e only d r a w b a c k p r e v a i l i n g with such t h e r m a l recording materials is that quantitative data r e g a r d i n g their sensitivities a n d linearity is not c o m m o n l y a v a i l a b l e 2. In this paper, a s i m p l e m e t h o d by which the t h r e s h o l d for r e c o r d i n g a n d the energy sensitivity of t h e r m o g r a p h i c materials can be d e t e r m i n e d experimentally, is described. A n analytical a p p r o a c h for estimating the energy sensitivities lot different types o f laser irradiation: either cw' or pulsed (with different pulse durations), is also presented. Using this The authors are at the Laser Laboratory, Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India. Received 25 March 1985. Revised 30 August 1985.
t e c h n i q u e a n u m b e r o f materials which can bc used lbr recording laser b e a m s t h e r m o g r a p h i c a l l y have been characterized. This m e t h o d o f c h a r a c t e r i z a t i o n can also be utilized lor the m e a s u r e m e n t of the d i a m e t e r of the laser b e a m as well as being of value in detecting and visualizing the b c a m a n d roughly assessing its intensity.
Description of the t e c h n i q u e In t h e r m o g r a p h i c recording` the formation of tile image occurs by the physical d e v e l o p m c n t of the material. This can be caused by m e l t i n g evaporation, b u r n i n g or s o m e o t h e r physical or c h e m i c a l c h a n g e in a thin surface layer. D u r i n g exposure, d e p e n d i n g on the a b s o r p t i o n coefficient b o f the recording medium, a localized heat source is lbrmed, the strength a n d extent of which d e p e n d s on the spatial a n d t e m p o r a l distribution o f the intensity 1 o f the laser beam. This heal source causes a r a p i d heating o f the irn=diatcd region, while the a d j a c e n t regions heat up gradually due to difl'usion. D e p e n d i n g on the m e c h a n i s m e m p l o y e d in the t h e r m a l i m a g i n g process, the local t e m p e r a t u r e T of the material has to reach a certain t h r e s h o l d 7"~,, as only above this does recording occur. | : o r example, if a b l a t i o n of the surface film is r e s p o n s i b l e tor recording, then Tc is tile v a p o r i z a t i o n t e m p e r a t u r e T~. C h a r a c t e r i z a t i o n of a t h c r m o g r a p h i c material then involves the m e a s u r e m e n t o f the t h r e s h o l d of energy anti e s t a b l i s h m e n t o f the functional
0030-3992/85/060297-06/$03.00 © 1985 Butterworth 8- Co (Publishers) Ltd OPTICS AND LASER TECHNOLOGY. DECEMBER 1985
297
relation between the subsequent increase in the image size with incident energy after this threshold is exceeded. Tile threshold intensity I c of the beam for thermal recording, however, depends on whether the laser is operated c o n t i n u o u s l y or pulsed a n d also on the duration of pulse or exposure. It is possible to c;llctllate thc energy 1: i rcquired for heating tile region to temperature Tu from t h e r m o d y n a m i c considerations alone ;is
l " i - mlC+(T<, - - To) -~ HI
(1)
where m is the mass of material in the rccorded spoL C the heat capacity. T0 the initial temperature, a n d H the heat of phasc t r a n s l o r m a t i o n ( a s s u m i n g Tc is the temperature at ,ahich a phase t r a n s f o r m a t i o n likc tnelting, occurs). But thc actual energy required will bc higher lh+.in this because the diffusion of heat causes a region largcr than just the rccorded spot to be healcd a n d also because of the radiative and convective heal losses lhal occur from the surfaces of the nledium. Hence the actual thresholds of energy will d e p e n d strongly on the thermal properties of the material such ;is the absorptivity, thcrlnal diffusion a n d conductivity, and also on the characteristics of tile beam such +.is its intensity distribution, power level, and duration. To estimate tile intensities a n d energy fluences n c c e s s a u for thermal recording on diffcrent material a simple analytical treatrucnt has been developed herc as she,an in thc next section. A s s u m i n g heat transl+cr to occur by c o n d u c t i o n only the temperature distribution within the material can be determined 3. If the threshold temperature at which the thermal record occurs is k n o w n then the shape of the thermal record formed can be found fronl the temperalure d i s t r i b u t i o n in lho material. Fig 1 shows schematically, the m a n n c l + in w h i c h the diameter of the record w o u l d increase with i n o 0 a s i n g intcnsit,< for a laser beam with Gaussiail d i s t r i b u t i o n (the dtlration of irradiation being taken +.is tile same for the three cases).
%,,
t
P
lai
- _ Eo,s--.-Et
J J
1 0 Rodius •
Fig. 1 Gaussian e n e r g y distribution in the laser beam. E t = threshold for recording, rb, 1 and rb, 2 = radii of records for E 1 and E 2
v+here./(l) Temperatu
re d i s t r i b u t i o n
The d i s t r i b u t i o n o f the ternpcrature w i t h i n a material irracliated b v ;.I laser bL'am c~ln be obtained by solving the time dependent heat c o n d u c t i o n equatioil 3'4 t'or a distributed heat source, subjected to a heal loss at the Il-ee surfaces exposed to the ambient atmosphere, l or the purposes of the estimate presented here a few siml+lil~'ing ;issumptions have been made. The recording n+ectium is considered opaque so thai all the absorption occttrs only at the surface, a c y l i n d r i c a l coordinate system ( r 0, z) is chosen with its o r i g i n at the surf;ice of the mediuin ;u+ld Cel+ltred on the optical axis of the laser beam. A n g u l a r symmetry is a s s u m e d so there is no dependence on tile 0 coordinate. |:or a laser operatii+~g in the TEM00 mode the intensity d i s t r i b u t i o n lit) is ;i (,i;iussian d i s t r i b u t i o n (as shown in l-ig. 1) given by l(r) = 10 c x p 1-21~Iw-+1
(2)
~ h c r e 10 is the intensity e l t h e laser beam at its centre (14'cm 2) and w is the beam radills. The strength of the hoe.It sotlrce,4 is then ,4(r --=(L t)
298
h l(r) f ( t )
(3)
describes tile time d e p e n d e n t nature of the laser pulse, t or a cw laser f(/) is unity and the solution of tile e q u a t i o n of c o n d u c t i o n yields5 0 - - tile d i m e n s i o n l e s s temperature rise. r
0(~, ~'. r) =
f/[r--c')
expI-~,,'(~'+l)l
0
expl-~/~t
Itz')~(r'+l)l
'dz' (4)
where the d i m e n s i o n l e s s variables 4, 5- r a n d @ are Z~= (2) '~ J/w, ¢ -
(2) '~ z/w, r -
~atA+~,
= ( S m !-" kT/(whlo) and where a is the thermal diffusivity/Cp(', k is the thermal conductivity, and p tile density of the material. The temperature at the centre of the heated region is O(0. 0. r ) - - 2 tan i (r)!:
(5)
and the actual temperature rise is T(0, 0. t) = Ibwlo/k(2rr)': I tan '(4al/w2) ':
OPTICS AND
LASER TECHNOLOGY.
DECEMBER
(6)
1985
5 . --
Silver
~
Graphite
-
-
~ ~ ~..~- "" ~ ~
~
~
-----
o~"~"-
Silver
~
Graphite
"
=
::
o
_~
/
///A"
"
_,,,y/~
I>"
/ ,."
,f
0.01
~
- - - PVC
2.o
/
z=O \~
~ I
///:,o~
~,
#=I
t.l.m
0.001
,¢
z=O.I mm i
~:
0.0001
I() 6
I0~
1(5 4
i6 3
16z Time ($)
o.I
I
I0
'r_
f=l
a
Fi0. 2 Maximum temperature rise (occurring at the centre of the beam I as a function of time for the three materials
Figure 2 shows thc temperature rise T(0, : t) as a function of the lime t of irradiation at the surface (z=0) as well as at several depths z along the centre of the beam, for three materials - - silver, graphite and .polyvinyl chloride. It can be seen that for some ranges ofl, ?$ is linear. This h a p p c n s whenever t is such that Z" ~ 0.1. that is. t a n - ' I S a t / w q " = ISat/w2l ~ a n d (5) becomes
~
1.0
o
I
z=1.0 mm
I
/
t:lO 3
1.0
t=l
8
6
4
2
O
2
4
6
8
rl w
(7)
T(O. O. t) = ( 2 b , / k ) lo(atlrr)"-
The rriaxirlmm temperature thai carl be reached at the beam centre is
(St
T(O. (i. oo ) = (rr/8)!~ (bl,/k)/O
In Fig, 3 the radial distribution of temperature with time as a p a r a m e t e r is shown. It is easy to infer that the region which is heated depends u p o n the l h e r m a l diffusivity a n d d u r a t i o n of irradiation, while the peak temperature reached d e p e n d s only on laser power a n d thermal conductivity.
Energy requirements
f
2m" expJ-2r21'wZ I d r - - n'21oAI
(9)
0
while for a pulsed h/ser (pulse a p p r o x i m a l e d by' a G a u s s i a n shape, width At) the pLilse energy is E=
~.2 ice /oAt
(10)
( ' o m p a r i n g (7). (9) a n d (10) it is seen thai for shorter pulse d u r a t i o n s At. lesser energy, is required lor the same recording.
Heat losses In oblainirig lhc above expressions for 7" no provision has been made for the possible occurrence of phase transformations, heal losses have also not been
OPTICS
AND
LASER
TECHNOLOGY.
included. If a phase change occurs belore lhe temperature Tc is reached on lhe surface then the analysis would have to be modified to lake into account the heat of phase t r a n s f o r m a t i o n and also the change in the properties of the new phase. Some studies where melting a n d vaporization have been taken into account are available5. but mostly these tire one d i m e n s i o n a l analyses. C o n s i d c r i n g heat h)sses to occur only from the surface exposed Io radiation the heat loss Q, is
Q, = 2rr
It is seen that the peak temperature at the surface increases as 1o t !-~(see (7)), whereas the beam energy is proportional to 10 t. Thus, to achieve the same T different beam energies fare required when either I0 or the d u r a t i o n t is changed. I[ for example, a cw laser is used for a period At, the total energy supplied is
E = A1
Fig. 3 Temperature distribution at the surface and other depths in the three materials heated by the laser beam
DECEMBER
1985
f~ le°'(T,~ - T.~) 0
+ h ( T s - - T.)I r d,"
( 1 I)
where lhc temperature of the surface T(r, - = O, t) is written as T~, T a is the a m b i e n t temperalure, e the equivalent emissivity5'6 which can be taken as approximalcly equal to h, o- lhe S t e f a n - B o l l z m a n n constank a n d t7 the convective heat loss coefficienP. While it is possible to solvc the unsteady equation of c o n d u c t i o n lor lhe material with the distributed heal source a n d the heal loss given by (2) a n d ( l i t such a solution is nol attempted here. On the other h a n d (I 1) is ulilized to obtain an estimate of lhc heal h)sses e n s u i n g fit any given temperalurc. In T a b l e t the rates arc listed of Ileal losses c o m p u t e d using ( 1 I) for a rtinge of centre line temperatures established in the material at time t. Since (I 1) gixes the tobit hcat Iosl from the surface, tar c o n v c r l i n g this n t l i l l b c r l o a t]ux value per unit tlrca, lhc lolal heal loss has been clividcd by the area o f the beam. Thus the llunlbers in ] a b l e 1 r c p r c s e n l a n ,:.lvcrage heal loss. It is evident Irom the hible [hal the heat losses are xcw small in c o m p a r i s o n to the incident irradiation excepl tar lhc case of vcry long periods o f i r r a d i a t i o n for a p o o r c o n d u c t o r o f heal
299
Table 1. Heat losses from a surface heated by a Gaussian laser beam Material: Graphite a=3.1 x 10-6m2s-l,b= 1.0, k = 5 W m -1 K-1 Temp (K) T(O, 0, t)
t = 10 -3 s Int*
t= 1 s
Loss**
Int*
( M W m -2) 500 1000 1500 2000 2500
43.2 86.4 129.7 172.9 216.1
t = 10 3 s
Loss**
Int*
( M W m -2)
0.002 0.014 0.056 0.156 0.389
5.35 10.70 16.05 21.40 26.75
Loss**
[lo, mi n
P t l - min
( M W m -2)
(VV)
3.99 7.98 11.97 15.96 19.95
12.5 25.1 37.6 50.1 62.7
( M W m -2)
0.006 0.039 0.133 0.348 0.767
4.78 9.56 14.34 19.11 23.89
0.018 0.092 0.251 0.571 1.158
Material: Silver a = 1.7 x 10 -4 m 2 s -1, b = 0.1, k = 4 1 9 t = 10 -3 s
Temp (K) 7-(0, O, t)
Int*
Loss**
t=
Int*
(GW m -2) 500 1000 1500 2000 2500
6.8 13.6 20.3 27.1 33.9
0.001 0.005 0.012 0.027 0.056
1 s
7(0, O, t)
t = 10 -3 s Int*
Loss**
( M W m -2) 500 1000 1500 2000 2500
8.5 17.1 25.6 34.2 42.7
0.002 0.014 0.050 0.148 0.337
Int*
(GW m -2)
s-l,
3.99 7.99 11.99 15.99 19.98
0.012 0.045 0.112 0.145 0.222
t = 10 3 s
Loss**
Int*
(kW m -2) 321 641 962 1282 1605
pttmi n
(GW m -2)
(kW)
3.34 6.69 10.03 13.37 16.72
10.5 21.0 31.5 42.0 52.5
b = 1 .O, k = 0.1 5 W m -1 K-1
t= 1 s Int*
Loss**
/1-o, mi n
(GW m -2)
0.010 0.037 0.073 0.122 0.197
Material: Black polyvinyl chloride a = 7 x 1 0-8 m 2 Temp(K)
t = 10 3 s
Loss**
4.06 8.11 12.17 16.22 20.28
W m -1 K-1
1.9 16.9 64.9 182.1 416.0
Loss**
/ t o, mi n
Ptlmi n
(kW m -2)
(W)
119 239 359 479 598
0.38 0.75 1.13 1.50 1.88
(kW m -2) 146 293 439 585 731
15 78 220 538 1083
*The value of /0 as calculated from (5) required to reach temperature T(O,O,t) after continuous irradiation for a duration At. All calculations in the above table have taken a laser beam radius w of 1 mm. **Heat loss due to convection and radiation from the top surface exposed to the laser, calculated using (1 1 ). Value of h, the convective heat transfer coefficient is taken to be 6 W m -2 K-1. The emissivity e is taken to be equal to b, the absorption coefficient. tThe asymptotic value of /0 as calculated from (8) required to reach temperature T(O,O,t) with continuous irradiation of infinite duration. ttThe total power of the laser necessary for raising the temperature to TlO,0,t ) with continuous irradiation of infinite duration. Total power Pmin = ma/2 /o,m,n"
like polyvinyl chloride. This shows that lhe neglect of heal losses is v e u well justified in most cases, espccially for short durations.
The energy density (tluence) E" t at the thrcshold for exposure for a G a u s s i a n beam is related to the threshold intensity It. n from (10) as {12)
For incident energy densities E "j > E "t, thermal imaging occurs giving rise to records of finite diameters r~ and r2 as for example in Fig t. when the incident
300
radius at which the intensity is I t, that is, from (2) I t = I0
Threshold energy
E " t = El~ rrwz - - rr': It. o A t
beam energy densities are E" 2 > E"~ > E"~. The radius rt, of the record for any intensity is n o t h i n g but the
expl-2 (,'#.)21
laking logarithms ln(/o) = In(lO + 2 ( O , / w ) 2
13)
I h u s for a given pulse length (or exposure duration with a cw laser) of At, if the incident energies are increased it is possible to generate images of increasmg diameters. T h e n since the relation between the energy densiiy a n d intensity is fixed (sec (12)) a plot of the log
OPTICS AND LASER TECHNOLOGY. DECEMBER 1985
T a b l e 2.
T h r e s h o l d e n e r g i e s and b e a m d i a m e t e r
Curve No (from Fig. 4)
Materials
Threshold (mJ cm -2)
Beam Radius w (mm)
1
Agfa Lithographic negative film, density 3.4*
1568.0
0.69
2
Agfa Brovira, Special printing paper BSI**
449.5
0.74
3
Black PVC sheet
312.0
0.76
4
Agfa Lithographic negative film, reverse side*
200.0
0.77
5
Agfa panchromatic 125 ASA negative film, density 2.6 t
62.0
0.73
6
Black Wrapping Paper
55.5
0.71
7
Kores "Carboplane 503' typing carbon sheet
15.0
0.78
*Lithographic film exposed to light, developed to density 3.4 **Printing paper exposed to light and developed to maximum density tpanchromatic 35 mm negative exposed and developed to density 2.6
of energy fluence against rh2 will result in a line whose intercept on the r - a x i s E"~ = r r !'~ ILo At, will be the t h r e s h o l d energy density a n d the slope o f the line will be the square o f the b e a m radius: w2.
Experimental results E x p e r i m e n t s were carried out for c h a r a c t e r i z i n g several c o m m o n l y a w d l a b l e m a t e r i a l s such as c a r b o n sheets,
sooo| 4 0 0 0 I--
•
I
exposed a n d d e v e l o p e d p h o t o g r a p h i c films, b l a c k p a p e r a n d plastic sheets. F o r these e x p e r i m e n t s a pulsed N d glass laserv o p e r a t i n g in TEMo0 m o d e was used. T h e laser was o p e r a t e d in the free r u n n i n g m o d e a n d its pulse d u r a t i o n was fixed at a b o u t 100 p,s. Pulse power a n d energy were m e a s u r e d using a c a l i b r a t e d p h o t o d i o d e ( E G & G Litemike). T h e m a t e r i a l s to be c h a r a c t e r i z e d were e x p o s e d to the b e a m whose intensity was c h a n g e d by i n c o r p o r a t i n g neutral density filters in the path. T a b l e 2 a n d Fig. 4 give the results o f the experiments. T h e intercept of the plot l n ( E " ) against r/,2 gives the t h r e s h o l d energy fluence. This t h r e s h o l d gives an i n d i c a t i o n of the m i n i m u m energy that can be detected a n d hence the suitability of the material for detecting or recording different ranges o f laser powers. T h e b e a m radius w found from the slopes o f the plot has also been listed in T a b l e 2.
Conclusions it has been shown above that the energy required for forming a record varies with pulse d u r a t i o n as l/At'~. Hence it is possible to infer the energy r e q u i r e m e n t for a pulse o f any arbitrary d u r a t i o n as long as no p h a s e c h a n g e occurs, or if the heat o f p h a s e transfer is very small. T h e analysis presented here is I o r a b e a m with G a u s s i a n intensity distribution. This is not a serious limitation a n d it is possible to carry out a s i m i l a r analysis for any a r b i t r a r y distribution, although p e r h a p s closed form solutions o f the type presented in (4) may not be possible. However, it s h o u l d be noted here that when phase t r a n s l b r m a t i o n (such as melting a n d evaporation) occurs the variation b e c o m e s much more c o m p l e x d e p e n d i n g as it would on the temperature, heat of t r a n s f o r m a t i o n and also on the differences in a a n d k between the first and s u b s e q u e n t phases.
2oo-
~
100
40--
20
0
I
I
I
I
I
I
I
2
3
4
5
6
r~2 x I03 Icmz)
7
References
Fig. 4 Results of experiments, The intercept on the y-axis is E t and slope of the line is square of the beam radius
OPTICS A N D LASER T E C H N O L O G Y .
Here it has been shown that this inexpensive a n d simple t e c h n i q u e for visualizing the b e a m can be m a d e quantitative and can be utilized for m e a s u r i n g the b e a m radius a n d even the energy of the beam. The m e a s u r e m e n t of b e a m d i a m e t e r needs only relative energy measurenaents, a n d hence this can be d o n e using neutral density filters.
DECEMBER 1985
I
Mitchel, G.R. Re~ Sci hl,~trum, 53, (19~2) I I I. MitcheL G., Grek, B., Martin, F., Pepin, H., Rheault, F., Baldis, H. J Phy.~
301
1), ,Ipl>l Phyx I I (197•) L153 2
OpL 17, (1978) 3527
3
Carlslaw, H.S., Jaeger, J.C. Conduction of heat in solids"
4
Ready, J.F. "[{fl'ecls of high pov, cr laser radiation" A c a d c m i c
Oxford Press (1947) Press (1971)
302
5
Sollid, J.E., Phipps, C.R., Thomas, S.J., MeLellan, E.J. Appl 6
7
l)uley,W.W. "('O 2 lasers, effects and applications'. Academic Press (1976) Kreith, F. "Principles of Heal T r a n s f e r 3rd F dilion lntext Educalional Publishers, New York (1976) Prasad, C.R., Veakateshan, S.P., Yoganarasimha, A. "Flash l.amp P u m p e d G l a s s Laser" l.aser Lab Report M E - I , L R - I . Indian lnst Science (1979)
OPTICS AND LASER TECHNOLOGY. DECEMBER 1 9 8 5
A simple technique for determining the energy sensitivities for the thermographic recording of laser beams is described. The principle behind this technique is that, if a laser beam with a known spatial distribution such as a Gaussian profile is used for imaging, the radius of the thermal image formed depends uniquely on the intensity of the impinging beam. Thus by measuring the radii of the images produced for different incident beam intensities the minimum intensity necessary (that is, the threshold) for thermographic imaging is found. The diameter of the laser beam can also be found from this measurement. A simple analysis based on the temperature distribution in the laser heated material shows that there is an inverse square root dependence on pulse duration or period of exposure for the energy fluence of the laser beam required, both for the threshold and the subsequent increase in the size of the recording. It has also been shown that except for low intensity, long duration exposure on very low conductivity materials, heat losses are not very significant. KEYVVORDS: lasers, thermographic recording, carbon photographic paper
Introduction The t h e r m a l r e c o r d i n g of laser b e a m s is utilized in m a n y applications, for example, in recording i n l b r m a t i o n on optical storage discs that have surfaces specially p r e p a r e d ibr u r i t i n g with m o d u l a t e d laser beams, a n d lor visualizing the b c a m s h a p e of infra-red lasers like N d : Y A G ( 1.06/xm) or C O 2 (10.6/,tin) on t h e r m a l l y sensitive m a t e r i a l s such as c a r b o n sheets or d e v c l o p e d p h o t o g r a p h i c papers. T h e latter a p p l i c a t i o n is a very' c o n v e n i e n t a n d inexpensive alternative to the c o n v e n t i o n a l m e t h o d of using infra-red sensitivc or sensitized' p a n c h r o m a t i c films, infra-red p h o s p h o r s , p h o t o d e t e c t o r ( s i l i c o n or pyroelectric) arrays or infrared vidicon cameras, etc, that arc expensive a n d often difficult to u s e T h e only d r a w b a c k p r e v a i l i n g with such t h e r m a l recording materials is that quantitative data r e g a r d i n g their sensitivities a n d linearity is not c o m m o n l y a v a i l a b l e 2. In this paper, a s i m p l e m e t h o d by which the t h r e s h o l d for r e c o r d i n g a n d the energy sensitivity of t h e r m o g r a p h i c materials can be d e t e r m i n e d experimentally, is described. A n analytical a p p r o a c h for estimating the energy sensitivities lot different types o f laser irradiation: either cw' or pulsed (with different pulse durations), is also presented. Using this The authors are at the Laser Laboratory, Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India. Received 25 March 1985. Revised 30 August 1985.
t e c h n i q u e a n u m b e r o f materials which can bc used lbr recording laser b e a m s t h e r m o g r a p h i c a l l y have been characterized. This m e t h o d o f c h a r a c t e r i z a t i o n can also be utilized lor the m e a s u r e m e n t of the d i a m e t e r of the laser b e a m as well as being of value in detecting and visualizing the b c a m a n d roughly assessing its intensity.
Description of the t e c h n i q u e In t h e r m o g r a p h i c recording` the formation of tile image occurs by the physical d e v e l o p m c n t of the material. This can be caused by m e l t i n g evaporation, b u r n i n g or s o m e o t h e r physical or c h e m i c a l c h a n g e in a thin surface layer. D u r i n g exposure, d e p e n d i n g on the a b s o r p t i o n coefficient b o f the recording medium, a localized heat source is lbrmed, the strength a n d extent of which d e p e n d s on the spatial a n d t e m p o r a l distribution o f the intensity 1 o f the laser beam. This heal source causes a r a p i d heating o f the irn=diatcd region, while the a d j a c e n t regions heat up gradually due to difl'usion. D e p e n d i n g on the m e c h a n i s m e m p l o y e d in the t h e r m a l i m a g i n g process, the local t e m p e r a t u r e T of the material has to reach a certain t h r e s h o l d 7"~,, as only above this does recording occur. | : o r example, if a b l a t i o n of the surface film is r e s p o n s i b l e tor recording, then Tc is tile v a p o r i z a t i o n t e m p e r a t u r e T~. C h a r a c t e r i z a t i o n of a t h c r m o g r a p h i c material then involves the m e a s u r e m e n t o f the t h r e s h o l d of energy anti e s t a b l i s h m e n t o f the functional
0030-3992/85/060297-06/$03.00 © 1985 Butterworth 8- Co (Publishers) Ltd OPTICS AND LASER TECHNOLOGY. DECEMBER 1985
297
relation between the subsequent increase in the image size with incident energy after this threshold is exceeded. Tile threshold intensity I c of the beam for thermal recording, however, depends on whether the laser is operated c o n t i n u o u s l y or pulsed a n d also on the duration of pulse or exposure. It is possible to c;llctllate thc energy 1: i rcquired for heating tile region to temperature Tu from t h e r m o d y n a m i c considerations alone ;is
l " i - mlC+(T<, - - To) -~ HI
(1)
where m is the mass of material in the rccorded spoL C the heat capacity. T0 the initial temperature, a n d H the heat of phasc t r a n s l o r m a t i o n ( a s s u m i n g Tc is the temperature at ,ahich a phase t r a n s f o r m a t i o n likc tnelting, occurs). But thc actual energy required will bc higher lh+.in this because the diffusion of heat causes a region largcr than just the rccorded spot to be healcd a n d also because of the radiative and convective heal losses lhal occur from the surfaces of the nledium. Hence the actual thresholds of energy will d e p e n d strongly on the thermal properties of the material such ;is the absorptivity, thcrlnal diffusion a n d conductivity, and also on the characteristics of tile beam such +.is its intensity distribution, power level, and duration. To estimate tile intensities a n d energy fluences n c c e s s a u for thermal recording on diffcrent material a simple analytical treatrucnt has been developed herc as she,an in thc next section. A s s u m i n g heat transl+cr to occur by c o n d u c t i o n only the temperature distribution within the material can be determined 3. If the threshold temperature at which the thermal record occurs is k n o w n then the shape of the thermal record formed can be found fronl the temperalure d i s t r i b u t i o n in lho material. Fig 1 shows schematically, the m a n n c l + in w h i c h the diameter of the record w o u l d increase with i n o 0 a s i n g intcnsit,< for a laser beam with Gaussiail d i s t r i b u t i o n (the dtlration of irradiation being taken +.is tile same for the three cases).
%,,
t
P
lai
- _ Eo,s--.-Et
J J
1 0 Rodius •
Fig. 1 Gaussian e n e r g y distribution in the laser beam. E t = threshold for recording, rb, 1 and rb, 2 = radii of records for E 1 and E 2
v+here./(l) Temperatu
re d i s t r i b u t i o n
The d i s t r i b u t i o n o f the ternpcrature w i t h i n a material irracliated b v ;.I laser bL'am c~ln be obtained by solving the time dependent heat c o n d u c t i o n equatioil 3'4 t'or a distributed heat source, subjected to a heal loss at the Il-ee surfaces exposed to the ambient atmosphere, l or the purposes of the estimate presented here a few siml+lil~'ing ;issumptions have been made. The recording n+ectium is considered opaque so thai all the absorption occttrs only at the surface, a c y l i n d r i c a l coordinate system ( r 0, z) is chosen with its o r i g i n at the surf;ice of the mediuin ;u+ld Cel+ltred on the optical axis of the laser beam. A n g u l a r symmetry is a s s u m e d so there is no dependence on tile 0 coordinate. |:or a laser operatii+~g in the TEM00 mode the intensity d i s t r i b u t i o n lit) is ;i (,i;iussian d i s t r i b u t i o n (as shown in l-ig. 1) given by l(r) = 10 c x p 1-21~Iw-+1
(2)
~ h c r e 10 is the intensity e l t h e laser beam at its centre (14'cm 2) and w is the beam radills. The strength of the hoe.It sotlrce,4 is then ,4(r --=(L t)
298
h l(r) f ( t )
(3)
describes tile time d e p e n d e n t nature of the laser pulse, t or a cw laser f(/) is unity and the solution of tile e q u a t i o n of c o n d u c t i o n yields5 0 - - tile d i m e n s i o n l e s s temperature rise. r
0(~, ~'. r) =
f/[r--c')
expI-~,,'(~'+l)l
0
expl-~/~t
Itz')~(r'+l)l
'dz' (4)
where the d i m e n s i o n l e s s variables 4, 5- r a n d @ are Z~= (2) '~ J/w, ¢ -
(2) '~ z/w, r -
~atA+~,
= ( S m !-" kT/(whlo) and where a is the thermal diffusivity/Cp(', k is the thermal conductivity, and p tile density of the material. The temperature at the centre of the heated region is O(0. 0. r ) - - 2 tan i (r)!:
(5)
and the actual temperature rise is T(0, 0. t) = Ibwlo/k(2rr)': I tan '(4al/w2) ':
OPTICS AND
LASER TECHNOLOGY.
DECEMBER
(6)
1985
5 . --
Silver
~
Graphite
-
-
~ ~ ~..~- "" ~ ~
~
~
-----
o~"~"-
Silver
~
Graphite
"
=
::
o
_~
/
///A"
"
_,,,y/~
I>"
/ ,."
,f
0.01
~
- - - PVC
2.o
/
z=O \~
~ I
///:,o~
~,
#=I
t.l.m
0.001
,¢
z=O.I mm i
~:
0.0001
I() 6
I0~
1(5 4
i6 3
16z Time ($)
o.I
I
I0
'r_
f=l
a
Fi0. 2 Maximum temperature rise (occurring at the centre of the beam I as a function of time for the three materials
Figure 2 shows thc temperature rise T(0, : t) as a function of the lime t of irradiation at the surface (z=0) as well as at several depths z along the centre of the beam, for three materials - - silver, graphite and .polyvinyl chloride. It can be seen that for some ranges ofl, ?$ is linear. This h a p p c n s whenever t is such that Z" ~ 0.1. that is. t a n - ' I S a t / w q " = ISat/w2l ~ a n d (5) becomes
~
1.0
o
I
z=1.0 mm
I
/
t:lO 3
1.0
t=l
8
6
4
2
O
2
4
6
8
rl w
(7)
T(O. O. t) = ( 2 b , / k ) lo(atlrr)"-
The rriaxirlmm temperature thai carl be reached at the beam centre is
(St
T(O. (i. oo ) = (rr/8)!~ (bl,/k)/O
In Fig, 3 the radial distribution of temperature with time as a p a r a m e t e r is shown. It is easy to infer that the region which is heated depends u p o n the l h e r m a l diffusivity a n d d u r a t i o n of irradiation, while the peak temperature reached d e p e n d s only on laser power a n d thermal conductivity.
Energy requirements
f
2m" expJ-2r21'wZ I d r - - n'21oAI
(9)
0
while for a pulsed h/ser (pulse a p p r o x i m a l e d by' a G a u s s i a n shape, width At) the pLilse energy is E=
~.2 ice /oAt
(10)
( ' o m p a r i n g (7). (9) a n d (10) it is seen thai for shorter pulse d u r a t i o n s At. lesser energy, is required lor the same recording.
Heat losses In oblainirig lhc above expressions for 7" no provision has been made for the possible occurrence of phase transformations, heal losses have also not been
OPTICS
AND
LASER
TECHNOLOGY.
included. If a phase change occurs belore lhe temperature Tc is reached on lhe surface then the analysis would have to be modified to lake into account the heat of phase t r a n s f o r m a t i o n and also the change in the properties of the new phase. Some studies where melting a n d vaporization have been taken into account are available5. but mostly these tire one d i m e n s i o n a l analyses. C o n s i d c r i n g heat h)sses to occur only from the surface exposed Io radiation the heat loss Q, is
Q, = 2rr
It is seen that the peak temperature at the surface increases as 1o t !-~(see (7)), whereas the beam energy is proportional to 10 t. Thus, to achieve the same T different beam energies fare required when either I0 or the d u r a t i o n t is changed. I[ for example, a cw laser is used for a period At, the total energy supplied is
E = A1
Fig. 3 Temperature distribution at the surface and other depths in the three materials heated by the laser beam
DECEMBER
1985
f~ le°'(T,~ - T.~) 0
+ h ( T s - - T.)I r d,"
( 1 I)
where lhc temperature of the surface T(r, - = O, t) is written as T~, T a is the a m b i e n t temperalure, e the equivalent emissivity5'6 which can be taken as approximalcly equal to h, o- lhe S t e f a n - B o l l z m a n n constank a n d t7 the convective heat loss coefficienP. While it is possible to solvc the unsteady equation of c o n d u c t i o n lor lhe material with the distributed heal source a n d the heal loss given by (2) a n d ( l i t such a solution is nol attempted here. On the other h a n d (I 1) is ulilized to obtain an estimate of lhc heal h)sses e n s u i n g fit any given temperalurc. In T a b l e t the rates arc listed of Ileal losses c o m p u t e d using ( 1 I) for a rtinge of centre line temperatures established in the material at time t. Since (I 1) gixes the tobit hcat Iosl from the surface, tar c o n v c r l i n g this n t l i l l b c r l o a t]ux value per unit tlrca, lhc lolal heal loss has been clividcd by the area o f the beam. Thus the llunlbers in ] a b l e 1 r c p r c s e n l a n ,:.lvcrage heal loss. It is evident Irom the hible [hal the heat losses are xcw small in c o m p a r i s o n to the incident irradiation excepl tar lhc case of vcry long periods o f i r r a d i a t i o n for a p o o r c o n d u c t o r o f heal
299
Table 1. Heat losses from a surface heated by a Gaussian laser beam Material: Graphite a=3.1 x 10-6m2s-l,b= 1.0, k = 5 W m -1 K-1 Temp (K) T(O, 0, t)
t = 10 -3 s Int*
t= 1 s
Loss**
Int*
( M W m -2) 500 1000 1500 2000 2500
43.2 86.4 129.7 172.9 216.1
t = 10 3 s
Loss**
Int*
( M W m -2)
0.002 0.014 0.056 0.156 0.389
5.35 10.70 16.05 21.40 26.75
Loss**
[lo, mi n
P t l - min
( M W m -2)
(VV)
3.99 7.98 11.97 15.96 19.95
12.5 25.1 37.6 50.1 62.7
( M W m -2)
0.006 0.039 0.133 0.348 0.767
4.78 9.56 14.34 19.11 23.89
0.018 0.092 0.251 0.571 1.158
Material: Silver a = 1.7 x 10 -4 m 2 s -1, b = 0.1, k = 4 1 9 t = 10 -3 s
Temp (K) 7-(0, O, t)
Int*
Loss**
t=
Int*
(GW m -2) 500 1000 1500 2000 2500
6.8 13.6 20.3 27.1 33.9
0.001 0.005 0.012 0.027 0.056
1 s
7(0, O, t)
t = 10 -3 s Int*
Loss**
( M W m -2) 500 1000 1500 2000 2500
8.5 17.1 25.6 34.2 42.7
0.002 0.014 0.050 0.148 0.337
Int*
(GW m -2)
s-l,
3.99 7.99 11.99 15.99 19.98
0.012 0.045 0.112 0.145 0.222
t = 10 3 s
Loss**
Int*
(kW m -2) 321 641 962 1282 1605
pttmi n
(GW m -2)
(kW)
3.34 6.69 10.03 13.37 16.72
10.5 21.0 31.5 42.0 52.5
b = 1 .O, k = 0.1 5 W m -1 K-1
t= 1 s Int*
Loss**
/1-o, mi n
(GW m -2)
0.010 0.037 0.073 0.122 0.197
Material: Black polyvinyl chloride a = 7 x 1 0-8 m 2 Temp(K)
t = 10 3 s
Loss**
4.06 8.11 12.17 16.22 20.28
W m -1 K-1
1.9 16.9 64.9 182.1 416.0
Loss**
/ t o, mi n
Ptlmi n
(kW m -2)
(W)
119 239 359 479 598
0.38 0.75 1.13 1.50 1.88
(kW m -2) 146 293 439 585 731
15 78 220 538 1083
*The value of /0 as calculated from (5) required to reach temperature T(O,O,t) after continuous irradiation for a duration At. All calculations in the above table have taken a laser beam radius w of 1 mm. **Heat loss due to convection and radiation from the top surface exposed to the laser, calculated using (1 1 ). Value of h, the convective heat transfer coefficient is taken to be 6 W m -2 K-1. The emissivity e is taken to be equal to b, the absorption coefficient. tThe asymptotic value of /0 as calculated from (8) required to reach temperature T(O,O,t) with continuous irradiation of infinite duration. ttThe total power of the laser necessary for raising the temperature to TlO,0,t ) with continuous irradiation of infinite duration. Total power Pmin = ma/2 /o,m,n"
like polyvinyl chloride. This shows that lhe neglect of heal losses is v e u well justified in most cases, espccially for short durations.
The energy density (tluence) E" t at the thrcshold for exposure for a G a u s s i a n beam is related to the threshold intensity It. n from (10) as {12)
For incident energy densities E "j > E "t, thermal imaging occurs giving rise to records of finite diameters r~ and r2 as for example in Fig t. when the incident
300
radius at which the intensity is I t, that is, from (2) I t = I0
Threshold energy
E " t = El~ rrwz - - rr': It. o A t
beam energy densities are E" 2 > E"~ > E"~. The radius rt, of the record for any intensity is n o t h i n g but the
expl-2 (,'#.)21
laking logarithms ln(/o) = In(lO + 2 ( O , / w ) 2
13)
I h u s for a given pulse length (or exposure duration with a cw laser) of At, if the incident energies are increased it is possible to generate images of increasmg diameters. T h e n since the relation between the energy densiiy a n d intensity is fixed (sec (12)) a plot of the log
OPTICS AND LASER TECHNOLOGY. DECEMBER 1985
T a b l e 2.
T h r e s h o l d e n e r g i e s and b e a m d i a m e t e r
Curve No (from Fig. 4)
Materials
Threshold (mJ cm -2)
Beam Radius w (mm)
1
Agfa Lithographic negative film, density 3.4*
1568.0
0.69
2
Agfa Brovira, Special printing paper BSI**
449.5
0.74
3
Black PVC sheet
312.0
0.76
4
Agfa Lithographic negative film, reverse side*
200.0
0.77
5
Agfa panchromatic 125 ASA negative film, density 2.6 t
62.0
0.73
6
Black Wrapping Paper
55.5
0.71
7
Kores "Carboplane 503' typing carbon sheet
15.0
0.78
*Lithographic film exposed to light, developed to density 3.4 **Printing paper exposed to light and developed to maximum density tpanchromatic 35 mm negative exposed and developed to density 2.6
of energy fluence against rh2 will result in a line whose intercept on the r - a x i s E"~ = r r !'~ ILo At, will be the t h r e s h o l d energy density a n d the slope o f the line will be the square o f the b e a m radius: w2.
Experimental results E x p e r i m e n t s were carried out for c h a r a c t e r i z i n g several c o m m o n l y a w d l a b l e m a t e r i a l s such as c a r b o n sheets,
sooo| 4 0 0 0 I--
•
I
exposed a n d d e v e l o p e d p h o t o g r a p h i c films, b l a c k p a p e r a n d plastic sheets. F o r these e x p e r i m e n t s a pulsed N d glass laserv o p e r a t i n g in TEMo0 m o d e was used. T h e laser was o p e r a t e d in the free r u n n i n g m o d e a n d its pulse d u r a t i o n was fixed at a b o u t 100 p,s. Pulse power a n d energy were m e a s u r e d using a c a l i b r a t e d p h o t o d i o d e ( E G & G Litemike). T h e m a t e r i a l s to be c h a r a c t e r i z e d were e x p o s e d to the b e a m whose intensity was c h a n g e d by i n c o r p o r a t i n g neutral density filters in the path. T a b l e 2 a n d Fig. 4 give the results o f the experiments. T h e intercept of the plot l n ( E " ) against r/,2 gives the t h r e s h o l d energy fluence. This t h r e s h o l d gives an i n d i c a t i o n of the m i n i m u m energy that can be detected a n d hence the suitability of the material for detecting or recording different ranges o f laser powers. T h e b e a m radius w found from the slopes o f the plot has also been listed in T a b l e 2.
Conclusions it has been shown above that the energy required for forming a record varies with pulse d u r a t i o n as l/At'~. Hence it is possible to infer the energy r e q u i r e m e n t for a pulse o f any arbitrary d u r a t i o n as long as no p h a s e c h a n g e occurs, or if the heat o f p h a s e transfer is very small. T h e analysis presented here is I o r a b e a m with G a u s s i a n intensity distribution. This is not a serious limitation a n d it is possible to carry out a s i m i l a r analysis for any a r b i t r a r y distribution, although p e r h a p s closed form solutions o f the type presented in (4) may not be possible. However, it s h o u l d be noted here that when phase t r a n s l b r m a t i o n (such as melting a n d evaporation) occurs the variation b e c o m e s much more c o m p l e x d e p e n d i n g as it would on the temperature, heat of t r a n s f o r m a t i o n and also on the differences in a a n d k between the first and s u b s e q u e n t phases.
2oo-
~
100
40--
20
0
I
I
I
I
I
I
I
2
3
4
5
6
r~2 x I03 Icmz)
7
References
Fig. 4 Results of experiments, The intercept on the y-axis is E t and slope of the line is square of the beam radius
OPTICS A N D LASER T E C H N O L O G Y .
Here it has been shown that this inexpensive a n d simple t e c h n i q u e for visualizing the b e a m can be m a d e quantitative and can be utilized for m e a s u r i n g the b e a m radius a n d even the energy of the beam. The m e a s u r e m e n t of b e a m d i a m e t e r needs only relative energy measurenaents, a n d hence this can be d o n e using neutral density filters.
DECEMBER 1985
I
Mitchel, G.R. Re~ Sci hl,~trum, 53, (19~2) I I I. MitcheL G., Grek, B., Martin, F., Pepin, H., Rheault, F., Baldis, H. J Phy.~
301
1), ,Ipl>l Phyx I I (197•) L153 2
OpL 17, (1978) 3527
3
Carlslaw, H.S., Jaeger, J.C. Conduction of heat in solids"
4
Ready, J.F. "[{fl'ecls of high pov, cr laser radiation" A c a d c m i c
Oxford Press (1947) Press (1971)
302
5
Sollid, J.E., Phipps, C.R., Thomas, S.J., MeLellan, E.J. Appl 6
7
l)uley,W.W. "('O 2 lasers, effects and applications'. Academic Press (1976) Kreith, F. "Principles of Heal T r a n s f e r 3rd F dilion lntext Educalional Publishers, New York (1976) Prasad, C.R., Veakateshan, S.P., Yoganarasimha, A. "Flash l.amp P u m p e d G l a s s Laser" l.aser Lab Report M E - I , L R - I . Indian lnst Science (1979)
OPTICS AND LASER TECHNOLOGY. DECEMBER 1 9 8 5