Thermal Blooming - Revision history

Lwcamp at 19:06, 7 March 2026

2026-03-07T19:06:55Z

← Older revision		Revision as of 12:06, 7 March 2026
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	==References==		==References==

	[[Category:Lasers]][[Category:Physics]][[Category:Heat]][[Category:Physics & Engineering]]		[[Category:Lasers]][[Category:Physics]][[Category:Heat]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Lwcamp at 01:19, 10 April 2025

2025-04-10T01:19:52Z

← Older revision		Revision as of 18:19, 9 April 2025
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	For pulsed beams, thermal blooming can be less of an issue. For one thing, the pulse is usually so fast that wind has a negligible effect. If your pulse length is shorter than your minimum beam diameter divided by the speed of sound, thermal blooming is much less of an issue because the air will not have had enough time to expand to make a lens. The equivalent of the thermal distortion factor N for pulsed beams are the parameters N<sub>l</sub> and N<sub>s</sub> for pulses long and short compared to the time for sound to cross their beam diameters, respectively.		For pulsed beams, thermal blooming can be less of an issue. For one thing, the pulse is usually so fast that wind has a negligible effect. If your pulse length is shorter than your minimum beam diameter divided by the speed of sound, thermal blooming is much less of an issue because the air will not have had enough time to expand to make a lens. The equivalent of the thermal distortion factor N for pulsed beams are the parameters N<sub>l</sub> and N<sub>s</sub> for pulses long and short compared to the time for sound to cross their beam diameters, respectively.
	<ref name=Kleiman_1973>H. Kleiman and R. W. O'Neil "Thermal blooming of pulsed laser radiation", Appl. Phys. Lett. 23, 43 (1973). N<sub>l</sub> differs by a factor of 2 from T<sub>lc</sub> and N<sub>s</sub> by a factor of 4 from T<sub>sc</sub> because those give the time-dependent change in the laser spot and we are interested in the total fluence dumped on the target during the time the spot is on. So the presented results are for time-averaging the T parameters.</ref>		<ref name=Kleiman_1973>H. Kleiman and R. W. O'Neil "Thermal blooming of pulsed laser radiation", Appl. Phys. Lett. 23, 43 (1973). N<sub>l</sub> differs by a factor of 2 from T<sub>lc</sub> and N<sub>s</sub> by a factor of 4 from T<sub>sc</sub> because those give the time-dependent change in the laser spot and we are interested in the total fluence dumped on the target during the time the spot is on. So the presented results are for time-averaging the T parameters.</ref>
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><~~math~~>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
	~~\begin{array}{lll}~~		<table>
	~~N_l &~~ = ~~& \dfrac{~~1}{6 ~~\pi} \, \dfrac{\beta \,~~ E \, R^2~~}{R_a \,~~ D^2 \, S^2~~} \\~~		<tr><td>N<sub>l</sub> <td> = <td align="left"> (1 / (6 π)) [(β E R<sup>2</sup>) / (R<sub>a</sub> D<sup>2</sup> S<sup>2</sup>)]
	~~N_s &~~ = ~~& \dfrac{~~1}{30 ~~\pi} \, \dfrac{\beta \,~~ E \, R^2 \, (t ~~\, c_s~~)^2~~}{R_a \,~~ D^2 \, S^4}		<tr><td>N<sub>s</sub> <td> = <td align="left"> (1 / (30 π)) [(β E R<sup>2</sup> (t c<sub>s</sub>)<sup>2</sup>) / (R<sub>a</sub> D<sup>2</sup> S<sup>4</sup>)]
	~~\end{array}~~		</table>
	</~~math~~></div>		</div>
	where ~~<math>~~E~~</math>~~ is the pulse energy, ~~<math>~~t~~</math>~~ is the pulse duration, <~~math~~>~~c_s~~</~~math~~> is the speed of sound (approximately 330 m/s in sea level air at shirt-sleeve temperatures). If ~~<math>~~D / ~~c_s~~ < t</~~math~~>, use <~~math~~>~~N_l~~</~~math~~>. If ~~<math>~~S / ~~c_s~~ > t</~~math~~>, use <~~math~~>~~N_s~~</~~math~~>. If you just happen to be somewhere between these, either take your best guess or get a grant, hire several grad students and post-docs, and perform the research to figure out the proper formula yourself. Again, if <~~math~~>~~N_l~~</~~math~~> or <~~math~~>~~N_s~~</~~math~~>, as appropriate, is less than one thermal blooming is not much of an issue. If they are, either use sophisticated non-linear adaptive optics beam controls or adjust your beam parameters so it is less than one.		where E is the pulse energy, t is the pulse duration, c<sub>s</sub> is the speed of sound (approximately 330 m/s in sea level air at shirt-sleeve temperatures). If D / c<sub>s</sub> < t, use N<sub>l</sub>. If S / c<sub>s</sub> > t, use N<sub>s</sub>. If you just happen to be somewhere between these, either take your best guess or get a grant, hire several grad students and post-docs, and perform the research to figure out the proper formula yourself. Again, if N<sub>l</sub> or N<sub>s</sub>, as appropriate, is less than one thermal blooming is not much of an issue. If they are greater than one, either use sophisticated non-linear adaptive optics beam controls or adjust your beam parameters so it is less than one.

	It is interesting to note that for [[Diffraction\|diffraction]]-limited beams, ~~<math>\frac{~~R}{S \, D~~}</math>~~ does not depend on distance so long as the beam is focused at the target. So a pulsed beam governed by <~~math~~>~~N_l~~</~~math~~> has the same amount of thermal blooming at any distance.		It is interesting to note that for [[Diffraction\|diffraction]]-limited beams, R / (S D) does not depend on distance so long as the beam is focused at the target. So a pulsed beam governed by N<sub>l</sub> has the same amount of thermal blooming at any distance.

	==Credit==		==Credit==

Lwcamp at 01:03, 10 April 2025

2025-04-10T01:03:51Z

← Older revision		Revision as of 18:03, 9 April 2025
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	where g is the acceleration due to gravity (g = 9.8 m/s² on Earth). Normally, however, if you are outside this will be small compared to any natural wind in the environment. And if you are inside the range is probably too short to matter.		where g is the acceleration due to gravity (g = 9.8 m/s² on Earth). Normally, however, if you are outside this will be small compared to any natural wind in the environment. And if you are inside the range is probably too short to matter.

	For pulsed beams, thermal blooming can be less of an issue. For one thing, the pulse is usually so fast that wind has a negligible effect. If your pulse length is shorter than your minimum beam diameter divided by the speed of sound, thermal blooming is much less of an issue because the air will not have had enough time to expand to make a lens. The equivalent of the thermal distortion factor ~~<math>~~N~~</math>~~ for pulsed beams are the parameters <~~math~~>~~N_l~~</~~math~~> and <~~math~~>~~N_s~~</~~math~~> for pulses long and short compared to the time for sound to cross their beam diameters, respectively.		For pulsed beams, thermal blooming can be less of an issue. For one thing, the pulse is usually so fast that wind has a negligible effect. If your pulse length is shorter than your minimum beam diameter divided by the speed of sound, thermal blooming is much less of an issue because the air will not have had enough time to expand to make a lens. The equivalent of the thermal distortion factor N for pulsed beams are the parameters N<sub>l</sub> and N<sub>s</sub> for pulses long and short compared to the time for sound to cross their beam diameters, respectively.
	<ref name=Kleiman_1973>H. Kleiman and R. W. O'Neil "Thermal blooming of pulsed laser radiation", Appl. Phys. Lett. 23, 43 (1973). <~~math~~>~~N_l~~</~~math~~> differs by a factor of 2 from <~~math~~>~~T_{~~lc}</~~math~~> and <~~math~~>~~N_s~~</~~math~~> by a factor of 4 from <~~math~~>~~T_sc~~</~~math~~> because those give the time-dependent change in the laser spot and we are interested in the total fluence dumped on the target during the time the spot is on. So the presented results are for time-averaging the ~~<math>~~T~~</math>~~ parameters.</ref>		<ref name=Kleiman_1973>H. Kleiman and R. W. O'Neil "Thermal blooming of pulsed laser radiation", Appl. Phys. Lett. 23, 43 (1973). N<sub>l</sub> differs by a factor of 2 from T<sub>lc</sub> and N<sub>s</sub> by a factor of 4 from T<sub>sc</sub> because those give the time-dependent change in the laser spot and we are interested in the total fluence dumped on the target during the time the spot is on. So the presented results are for time-averaging the T parameters.</ref>
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>
	\begin{array}{lll}		\begin{array}{lll}

Lwcamp at 00:59, 10 April 2025

2025-04-10T00:59:21Z

← Older revision		Revision as of 17:59, 9 April 2025
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	v<sub>convection</sub> = ( (2 P g) / (ρ C<sub>P</sub> R<sub>a</sub> T) )<sup>1/3</sup>		v<sub>convection</sub> = ( (2 P g) / (ρ C<sub>P</sub> R<sub>a</sub> T) )<sup>1/3</sup>
	</div>		</div>
	where ~~<math>~~g = 9.8 ~~\, \mbox{~~m}/~~\mbox{~~s~~}^2</math> is the acceleration due to gravity~~. Normally, however, if you are outside this will be small compared to any natural wind in the environment. And if you are inside the range is probably too short to matter.		where g is the acceleration due to gravity (g = 9.8 m/s² on Earth). Normally, however, if you are outside this will be small compared to any natural wind in the environment. And if you are inside the range is probably too short to matter.

	For pulsed beams, thermal blooming can be less of an issue. For one thing, the pulse is usually so fast that wind has a negligible effect. If your pulse length is shorter than your minimum beam diameter divided by the speed of sound, thermal blooming is much less of an issue because the air will not have had enough time to expand to make a lens. The equivalent of the thermal distortion factor <math>N</math> for pulsed beams are the parameters <math>N_l</math> and <math>N_s</math> for pulses long and short compared to the time for sound to cross their beam diameters, respectively.		For pulsed beams, thermal blooming can be less of an issue. For one thing, the pulse is usually so fast that wind has a negligible effect. If your pulse length is shorter than your minimum beam diameter divided by the speed of sound, thermal blooming is much less of an issue because the air will not have had enough time to expand to make a lens. The equivalent of the thermal distortion factor <math>N</math> for pulsed beams are the parameters <math>N_l</math> and <math>N_s</math> for pulses long and short compared to the time for sound to cross their beam diameters, respectively.

Lwcamp at 00:58, 10 April 2025

2025-04-10T00:58:09Z

← Older revision		Revision as of 17:58, 9 April 2025
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	If there is no wind speed, you can take the speed at which the heated air rises out of the beam path (a process known as convection) instead.		If there is no wind speed, you can take the speed at which the heated air rises out of the beam path (a process known as convection) instead.
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><~~math~~>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
	~~v_{\mbox{~~convection}} = ~~\left~~( ~~\frac{~~2 \, P \, g~~}{\rho \, C_P \, R_a \,~~ T~~} \right~~)^{1/3}		v<sub>convection</sub> = ( (2 P g) / (ρ C<sub>P</sub> R<sub>a</sub> T) )<sup>1/3</sup>
	</~~math~~></div>		</div>
	where <math>g = 9.8 \, \mbox{m}/\mbox{s}^2</math> is the acceleration due to gravity. Normally, however, if you are outside this will be small compared to any natural wind in the environment. And if you are inside the range is probably too short to matter.		where <math>g = 9.8 \, \mbox{m}/\mbox{s}^2</math> is the acceleration due to gravity. Normally, however, if you are outside this will be small compared to any natural wind in the environment. And if you are inside the range is probably too short to matter.

Lwcamp at 00:46, 10 April 2025

2025-04-10T00:46:34Z

← Older revision		Revision as of 17:46, 9 April 2025
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	The parameter β is the atmospheric thermal coefficient		The parameter β is the atmospheric thermal coefficient
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"~~><math~~>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
	~~\beta~~ = ~~\frac{~~(-dn/dT)~~}{\rho \, C_P}~~		β = (-dn/dT) / (ρ C<sub>P</sub>)
	</~~math~~></div>		</div>
	where ~~<math>~~dn/dT~~</math>~~ is the rate of change of the refractive index with increasing temperature, ~~<math>\rho</math>~~ is the air’s mass density, <~~math~~>~~C_P~~</~~math~~> is the specific heat capacity of the air at constant pressure, and ~~<math>\beta</math>~~ in sea level air on earth under typical conditions at visible and near visible wavelengths is around ~~<math>\beta~~ = 8.3 \times 10^{-10~~} \mbox{~~m~~}^3~~/~~\mbox{~~J~~}</math>~~.		where dn/dT is the rate of change of the refractive index with increasing temperature, ρ is the air’s mass density, C<sub>P</sub> is the specific heat capacity of the air at constant pressure, and β in sea level air on earth under typical conditions at visible and near visible wavelengths is around β = 8.3 × 10<sup>-10</sup> m³/J.

	If there is no wind speed, you can take the speed at which the heated air rises out of the beam path (a process known as convection) instead.		If there is no wind speed, you can take the speed at which the heated air rises out of the beam path (a process known as convection) instead.

Lwcamp at 00:43, 10 April 2025

2025-04-10T00:43:15Z

@@ Line 11: / Line 11: @@
 <ref name=Gebhardt_1990>Frederick Gebhardt, “Twenty-five years of thermal blooming: an overview”, Proc. SPIE 1221, Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, (1 May 1990); doi: 10.1117/12.18326</ref>
 (Warning! Math ahead!)
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 <table>
@@ Line 19: / Line 18: @@
 <tr>                                  <td align="left">(2 / N<sub>E</sub>&sup2;) [N<sub>E</sub> - 1 + exp(-N<sub>E</sub>)] otherwise
 <tr><td> N<sub>F</sub> <td> = <td align="left"> (π/4) n D / S
-<tr><td rowspan=2> q <td rowspan=2> = <td align="left">1 if N<sub>F</sub> = 0
+<tr><td rowspan=2> q <td rowspan=2> = <td align="left">1 if N<sub>F</sub> = 1
 <tr>                                  <td align="left">[(2 N<sub>F</sub>&sup2;) / (N<sub>F</sub> - 1)] [1 - ln(N<sub>F</sub>)/(N<sub>F</sub> - 1)] otherwise
 <tr><td> N<sub>V</sub> <td> = <td align="left"> v<sub>T</sub> / v
-<!--
+<tr><td rowspan=2> s <td rowspan=2> = <td align="left">1 if N<sub>V</sub> = 1
-N_V & = & v_T/v \\
+<tr>                                  <td align="left">[2 / (N<sub>V</sub> - 1)&sup2;] [N<sub>V</sub> ln(N<sub>V</sub>) - (N<sub>V</sub> - 1)] otherwise
-s & = & \left\{
+<tr><td> N <td> = <td align="left"> N<sub>c</sub> f q s
 </table>
 </div>
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>
+The parameter β is the atmospheric thermal coefficient
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>
 \beta = \frac{(-dn/dT)}{\rho \, C_P}

Lwcamp at 00:35, 10 April 2025

2025-04-10T00:35:35Z

← Older revision		Revision as of 17:35, 9 April 2025
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	<tr><td rowspan=2> f <td rowspan=2> = <td align="left">1 if N<sub>E</sub> = 0		<tr><td rowspan=2> f <td rowspan=2> = <td align="left">1 if N<sub>E</sub> = 0
	<tr> <td align="left">(2 / N<sub>E</sub>²) [N<sub>E</sub> - 1 + exp(-N<sub>E</sub>)] otherwise		<tr> <td align="left">(2 / N<sub>E</sub>²) [N<sub>E</sub> - 1 + exp(-N<sub>E</sub>)] otherwise
	<tr><td> N<sub>f</sub> <td> = <td align="left"> (π/4) n D / S		<tr><td> N<sub>F</sub> <td> = <td align="left"> (π/4) n D / S
			<tr><td rowspan=2> q <td rowspan=2> = <td align="left">1 if N<sub>F</sub> = 0
			<tr> <td align="left">[(2 N<sub>F</sub>²) / (N<sub>F</sub> - 1)] [1 - ln(N<sub>F</sub>)/(N<sub>F</sub> - 1)] otherwise
			<tr><td> N<sub>V</sub> <td> = <td align="left"> v<sub>T</sub> / v
	<!--		<!--
	~~N_F & = & \dfrac{\pi}{4} \, n \, \dfrac{D}{S} \\~~
	~~q & = & \left\{~~
	~~\begin{array}{ll}~~
	~~1 & \mbox{if } N_F = 1 \\~~
	~~\dfrac{2 \, N_F^2}{N_F - 1} \, \left( 1 - \dfrac{\ln[N_F]}{N_F - 1} \right)& \mbox{otherwise}~~
	~~\end{array}~~
	~~\right. \\~~
	N_V & = & v_T/v \\		N_V & = & v_T/v \\
	s & = & \left\{		s & = & \left\{

Lwcamp at 00:28, 10 April 2025

2025-04-10T00:28:21Z

@@ Line 6: / Line 6: @@
 Adaptive optics methods can help to solve this, but would-be laser engineers need to be careful because a straightforward implementation just ends up making the problem worse (to counteract the expansion, you focus the beam more which heats up the air more which makes your beam diverge even more).  Alternatively, you can use high power laser pulses that are so short that the air does not have time to expand.
-Does your beam need to worry about thermal blooming?  For relatively long duration beams moving relative to the air you can compute the <i>thermal distortion factor</i>, <math>N</math>, to find out.  If <math>N</math> is less than one, you can ignore thermal blooming.  If <math>N</math> is greater than this, you will need to correct for blooming if you want to keep a tight spot size. The larger <math>N</math>, the more difficult the blooming will be to correct.
+Does your beam need to worry about thermal blooming?  For relatively long duration beams moving relative to the air you can compute the <i>thermal distortion factor</i>, N, to find out.  If N is less than one, you can ignore thermal blooming.  If N is greater than this, you will need to correct for blooming if you want to keep a tight spot size. The larger N, the more difficult the blooming will be to correct.
-To compute <math>N</math>
+To compute N
 <ref name=Gebhardt_1990>Frederick Gebhardt, “Twenty-five years of thermal blooming: an overview”, Proc. SPIE 1221, Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, (1 May 1990); doi: 10.1117/12.18326</ref>
 (Warning! Math ahead!)
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>
 \begin{array}{lll}

Tshhmon at 21:55, 23 April 2024

2024-04-23T21:55:22Z

← Older revision		Revision as of 14:55, 23 April 2024
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	==References==		==References==

	[[Category:Lasers]]		[[Category:Lasers]][[Category:Physics]][[Category:Heat]][[Category:Physics & Engineering]]