Abstract

Read and bias power levels are capable of noticeably altering the response of thermomagnetooptic recording materials. The heating caused by the read power can decrease signal levels due to the temperature dependence of the polar Kerr rotation. Preheating caused by bias power levels also influences media sensitivity and responses during the writing process. Increased bias levels reduce the optimum recording power and increase the severity of mark length variations caused by write power fluctuations. Simple predictive expressions were derived to describe the influence of bias and read power levels during the mark formation and readout processes. The predicted results were in good qualitative and quantitative agreement with experimental observations.

© 1990 Optical Society of America

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References

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  1. W. A. Michael, D. Treves, “The Heat Problem in Magneto-Optic Readout,” J. Appl. Phys. 40, 303–311 (1969).
    [CrossRef]
  2. M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).
  3. K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
    [CrossRef]
  4. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).
  5. H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).
  6. B. J. Bartholomeusz, “Thermomagnetic Marking of Rare Earth–Transition Metal Thin Films,” J. Appl. Phys. 65, 262–268 (1989).
    [CrossRef]
  7. M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Laser-Induced Local Heating of Multilayers,” Appl. Opt. 21, 1106–1114 (1982).
    [CrossRef] [PubMed]
  8. R. Kant, “Laser-Induced Heating of a Multilayered Medium Resting on a Half Space. Part 1.—Stationary Source,” J. Appl. Mech. 55, 93–97 (1988).
    [CrossRef]
  9. E. V. LaBudde, R. A. LaBudde, C. M. Shevlin, “Theoretical Modeling, Calculations and Experiments Characterizing the Laser-Induced Hole-Formation of an In-Contact Overcoated Optical Disk Medium,” Proc. Soc. Photo-Opt. Instrum. Eng. 382, 116–148 (1983).
  10. J. Corcoran, H. Ferrier, “Melting Holes in Metal Films for Real-Time, High Density Digital Data Storage,” Proc. Soc. Photo-Opt. Instrum. Eng. 123, 1–31 (1977).
  11. B. J. Bartholomeusz, P. Bowers, D. Genova, “Simple Predictive Models for the Thermal Response of Optical Data Storage Media,” J. Appl. Phys. 66, 4635–4639 (1989).
    [CrossRef]
  12. M. Mansuripur, G. A. N. Connell, “Energetics of Domain Formation in Thermomagnetic Recording,” J. Appl. Phys. 55, 3049–3055 (1984).
    [CrossRef]
  13. P. Hansen, “Thermomagnetic Switching in Amorphous Rare-Earth Transition-Metal Alloys,” J. Appl. Phys. 62, 216–230 (1987).
    [CrossRef]
  14. M. Meichle, Eastman Kodak Co., Unpublished results (1989).
  15. A. H. M. Holtslag, “Calculations on Temperature Profiles in Optical Recording,” J. Appl. Phys. 66, 1530–1543 (1989).
    [CrossRef]
  16. M. K. Battacharya, Z. J. Cendes, “Finite-Element Modeling of Laser Beam Heating of Magnetic Films,” J. Appl. Phys. 57, 3894–3896 (1985).
    [CrossRef]

1989

K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
[CrossRef]

B. J. Bartholomeusz, “Thermomagnetic Marking of Rare Earth–Transition Metal Thin Films,” J. Appl. Phys. 65, 262–268 (1989).
[CrossRef]

B. J. Bartholomeusz, P. Bowers, D. Genova, “Simple Predictive Models for the Thermal Response of Optical Data Storage Media,” J. Appl. Phys. 66, 4635–4639 (1989).
[CrossRef]

A. H. M. Holtslag, “Calculations on Temperature Profiles in Optical Recording,” J. Appl. Phys. 66, 1530–1543 (1989).
[CrossRef]

1988

R. Kant, “Laser-Induced Heating of a Multilayered Medium Resting on a Half Space. Part 1.—Stationary Source,” J. Appl. Mech. 55, 93–97 (1988).
[CrossRef]

1987

H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

P. Hansen, “Thermomagnetic Switching in Amorphous Rare-Earth Transition-Metal Alloys,” J. Appl. Phys. 62, 216–230 (1987).
[CrossRef]

1985

M. K. Battacharya, Z. J. Cendes, “Finite-Element Modeling of Laser Beam Heating of Magnetic Films,” J. Appl. Phys. 57, 3894–3896 (1985).
[CrossRef]

1984

M. Mansuripur, G. A. N. Connell, “Energetics of Domain Formation in Thermomagnetic Recording,” J. Appl. Phys. 55, 3049–3055 (1984).
[CrossRef]

1983

E. V. LaBudde, R. A. LaBudde, C. M. Shevlin, “Theoretical Modeling, Calculations and Experiments Characterizing the Laser-Induced Hole-Formation of an In-Contact Overcoated Optical Disk Medium,” Proc. Soc. Photo-Opt. Instrum. Eng. 382, 116–148 (1983).

1982

1977

J. Corcoran, H. Ferrier, “Melting Holes in Metal Films for Real-Time, High Density Digital Data Storage,” Proc. Soc. Photo-Opt. Instrum. Eng. 123, 1–31 (1977).

1969

W. A. Michael, D. Treves, “The Heat Problem in Magneto-Optic Readout,” J. Appl. Phys. 40, 303–311 (1969).
[CrossRef]

Ashida, S.

K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
[CrossRef]

Bartholomeusz, B. J.

B. J. Bartholomeusz, “Thermomagnetic Marking of Rare Earth–Transition Metal Thin Films,” J. Appl. Phys. 65, 262–268 (1989).
[CrossRef]

B. J. Bartholomeusz, P. Bowers, D. Genova, “Simple Predictive Models for the Thermal Response of Optical Data Storage Media,” J. Appl. Phys. 66, 4635–4639 (1989).
[CrossRef]

Battacharya, M. K.

M. K. Battacharya, Z. J. Cendes, “Finite-Element Modeling of Laser Beam Heating of Magnetic Films,” J. Appl. Phys. 57, 3894–3896 (1985).
[CrossRef]

Bowers, P.

B. J. Bartholomeusz, P. Bowers, D. Genova, “Simple Predictive Models for the Thermal Response of Optical Data Storage Media,” J. Appl. Phys. 66, 4635–4639 (1989).
[CrossRef]

Cendes, Z. J.

M. K. Battacharya, Z. J. Cendes, “Finite-Element Modeling of Laser Beam Heating of Magnetic Films,” J. Appl. Phys. 57, 3894–3896 (1985).
[CrossRef]

Connell, G. A. N.

M. Mansuripur, G. A. N. Connell, “Energetics of Domain Formation in Thermomagnetic Recording,” J. Appl. Phys. 55, 3049–3055 (1984).
[CrossRef]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Laser-Induced Local Heating of Multilayers,” Appl. Opt. 21, 1106–1114 (1982).
[CrossRef] [PubMed]

Corcoran, J.

J. Corcoran, H. Ferrier, “Melting Holes in Metal Films for Real-Time, High Density Digital Data Storage,” Proc. Soc. Photo-Opt. Instrum. Eng. 123, 1–31 (1977).

Ferrier, H.

J. Corcoran, H. Ferrier, “Melting Holes in Metal Films for Real-Time, High Density Digital Data Storage,” Proc. Soc. Photo-Opt. Instrum. Eng. 123, 1–31 (1977).

Genova, D.

B. J. Bartholomeusz, P. Bowers, D. Genova, “Simple Predictive Models for the Thermal Response of Optical Data Storage Media,” J. Appl. Phys. 66, 4635–4639 (1989).
[CrossRef]

Goodman, J. W.

Hansen, P.

P. Hansen, “Thermomagnetic Switching in Amorphous Rare-Earth Transition-Metal Alloys,” J. Appl. Phys. 62, 216–230 (1987).
[CrossRef]

Hasegawa, H.

K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
[CrossRef]

Holtslag, A. H. M.

A. H. M. Holtslag, “Calculations on Temperature Profiles in Optical Recording,” J. Appl. Phys. 66, 1530–1543 (1989).
[CrossRef]

Ichihara, K.

K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
[CrossRef]

Kant, R.

R. Kant, “Laser-Induced Heating of a Multilayered Medium Resting on a Half Space. Part 1.—Stationary Source,” J. Appl. Mech. 55, 93–97 (1988).
[CrossRef]

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).

Kobori, H.

K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
[CrossRef]

LaBudde, E. V.

E. V. LaBudde, R. A. LaBudde, C. M. Shevlin, “Theoretical Modeling, Calculations and Experiments Characterizing the Laser-Induced Hole-Formation of an In-Contact Overcoated Optical Disk Medium,” Proc. Soc. Photo-Opt. Instrum. Eng. 382, 116–148 (1983).

LaBudde, R. A.

E. V. LaBudde, R. A. LaBudde, C. M. Shevlin, “Theoretical Modeling, Calculations and Experiments Characterizing the Laser-Induced Hole-Formation of an In-Contact Overcoated Optical Disk Medium,” Proc. Soc. Photo-Opt. Instrum. Eng. 382, 116–148 (1983).

Maeda, T.

H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).

Mansuripur, M.

M. Mansuripur, G. A. N. Connell, “Energetics of Domain Formation in Thermomagnetic Recording,” J. Appl. Phys. 55, 3049–3055 (1984).
[CrossRef]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Laser-Induced Local Heating of Multilayers,” Appl. Opt. 21, 1106–1114 (1982).
[CrossRef] [PubMed]

Meichle, M.

M. Meichle, Eastman Kodak Co., Unpublished results (1989).

Michael, W. A.

W. A. Michael, D. Treves, “The Heat Problem in Magneto-Optic Readout,” J. Appl. Phys. 40, 303–311 (1969).
[CrossRef]

Mitani, T.

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

Ojima, M.

H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).

Sato, M.

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

Shevlin, C. M.

E. V. LaBudde, R. A. LaBudde, C. M. Shevlin, “Theoretical Modeling, Calculations and Experiments Characterizing the Laser-Induced Hole-Formation of an In-Contact Overcoated Optical Disk Medium,” Proc. Soc. Photo-Opt. Instrum. Eng. 382, 116–148 (1983).

Sukeda, H.

H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).

Takahashi, M.

H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).

Tastukawa, S.

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

Toba, H.

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

Treves, D.

W. A. Michael, D. Treves, “The Heat Problem in Magneto-Optic Readout,” J. Appl. Phys. 40, 303–311 (1969).
[CrossRef]

Tsukane, N.

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

Appl. Opt.

J. Appl. Mech.

R. Kant, “Laser-Induced Heating of a Multilayered Medium Resting on a Half Space. Part 1.—Stationary Source,” J. Appl. Mech. 55, 93–97 (1988).
[CrossRef]

J. Appl. Phys.

W. A. Michael, D. Treves, “The Heat Problem in Magneto-Optic Readout,” J. Appl. Phys. 40, 303–311 (1969).
[CrossRef]

B. J. Bartholomeusz, P. Bowers, D. Genova, “Simple Predictive Models for the Thermal Response of Optical Data Storage Media,” J. Appl. Phys. 66, 4635–4639 (1989).
[CrossRef]

M. Mansuripur, G. A. N. Connell, “Energetics of Domain Formation in Thermomagnetic Recording,” J. Appl. Phys. 55, 3049–3055 (1984).
[CrossRef]

P. Hansen, “Thermomagnetic Switching in Amorphous Rare-Earth Transition-Metal Alloys,” J. Appl. Phys. 62, 216–230 (1987).
[CrossRef]

B. J. Bartholomeusz, “Thermomagnetic Marking of Rare Earth–Transition Metal Thin Films,” J. Appl. Phys. 65, 262–268 (1989).
[CrossRef]

A. H. M. Holtslag, “Calculations on Temperature Profiles in Optical Recording,” J. Appl. Phys. 66, 1530–1543 (1989).
[CrossRef]

M. K. Battacharya, Z. J. Cendes, “Finite-Element Modeling of Laser Beam Heating of Magnetic Films,” J. Appl. Phys. 57, 3894–3896 (1985).
[CrossRef]

Jpn. J. Appl. Phys.

H. Sukeda, M. Ojima, M. Takahashi, T. Maeda, “High-Density Magneto-Optic Disk Using Highly Controlled Pit-Edge Recording,” Jpn. J. Appl. Phys. 26, 243–248 (1987).

M. Sato, S. Tastukawa, N. Tsukane, T. Mitani, H. Toba, “NdDyFeCo for High Performance Magneto-Optical Disk,” Jpn. J. Appl. Phys. 26, 19–22 (1987).

Mater. Res. Soc. Symp. Proc.

K. Ichihara, S. Ashida, H. Kobori, H. Hasegawa, “Dependence of the Magneto-Optical Readout Signal on Readout Power and External Field,” Mater. Res. Soc. Symp. Proc. 150, 153–158 (1989).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

E. V. LaBudde, R. A. LaBudde, C. M. Shevlin, “Theoretical Modeling, Calculations and Experiments Characterizing the Laser-Induced Hole-Formation of an In-Contact Overcoated Optical Disk Medium,” Proc. Soc. Photo-Opt. Instrum. Eng. 382, 116–148 (1983).

J. Corcoran, H. Ferrier, “Melting Holes in Metal Films for Real-Time, High Density Digital Data Storage,” Proc. Soc. Photo-Opt. Instrum. Eng. 123, 1–31 (1977).

Other

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).

M. Meichle, Eastman Kodak Co., Unpublished results (1989).

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Figures (16)

Fig. 1
Fig. 1

Relative temperature distributions associated with the bias and write power levels in the vicinity of a mark. Adiabatic, loss free medium, write pulse length = 2 μm, and Pb = 0.2Pw.

Fig. 2
Fig. 2

Calculated (solid lines) and measured mark length error (in microns) as a function of write power for various read (= bias) power levels. RE–TM thin film on an ungrooved glass substrate. Scanning velocity = 5.5 m/s, write pulse length = 2.5 μm, and applied field = 300 Oe.

Fig. 3
Fig. 3

Calculated (solid lines) and measured mark length error (in microns) as a function of write power for scanning velocities of 5 and 10 m/s. RE–TM thin film on an ungrooved glass substrate. Write pulse length = 2 μm, read (= bias) power level = 1.6 mW, and applied field = 300 Oe.

Fig. 4
Fig. 4

Calculated and measured mark length error (in microns) as a function of write power for read power levels of 1.5 and 2.5 mW. The solid and broken lines are, respectively, the predictions of Eq. (9) with and without the incorporation of the bias power which equaled the read power in each case. RE–TM thin film on an ungrooved glass substrate. Scanning velocity = 5.5 m/s, write pulse length = 2.5 μm, and applied field = 300 Oe.

Fig. 5
Fig. 5

Calculated and measured slopes of the TIA power series response (at ORP) as a function of read (= bias) power level. RE–TM thin film on an ungrooved glass substrate. Write pulse length = 3.5 μm, scanning velocity = 7 m/s, and applied field = 300 Oe.

Fig. 6
Fig. 6

Mark length variability (normalized) as a function of bias power level. Read power = 2 mW in all cases. RE–TM thin film on an ungrooved glass substrate. Write pulse length = 3.5 μm, scanning velocity = 12 m/s, and applied field = 300 Oe.

Fig. 7
Fig. 7

Calculated [from expression (13)] and measured ORPs for a wide variety of RE–TM samples at various scanning velocities. In all cases, the write–pulse length exceeds 1.5 μm, the read (= bias) power = 1.8 mW, and the applied field = 300 Oe. The broken lines represent deviations of ±0.75 mW from the predicted values.

Fig. 8
Fig. 8

Measured Pth and ORPr as a function of read (= bias) power levels for a RE–TM film on an ungrooved glass substrate. Write pulse length = 2.5 μm, scanning velocity = 5.5 m/s, and applied field = 300 Oe. The broken lines represent slopes predicted by Eqs. (5) and (13), and the solid lines are least-squared fits to the data points.

Fig. 9
Fig. 9

Temperature dependence of the Kerr rotation θk for various terbium concentrations in amorphous Tbx(Fe95Co5)(1−x). Kerr angles normalized to unity at 20°C.

Fig. 10
Fig. 10

Calculated (solid line) and measured (points) dependence of the reduced Kerr rotation [θk(T)/θk(0 K)] on the reduced temperature (T/TCurie) for Tb25(Fe95Co5)75.

Fig. 11
Fig. 11

Calculated (solid line) and measured carrier levels as a function of read power level. RE–TM thin film on an ungrooved glass substrate, scanning velocity = 5.5 m/s, bias power level fixed at 2 mW, and applied field = 300 Oe. Calculated values normalized to measured value at 1.75-mW read power for comparative purposes.

Fig. 12
Fig. 12

Calculated maximum mark width as a function of bias power level for a RE–TM thin film on an ungrooved glass substrate. Scanning velocity = 5.5 m/s and measured threshold write power ≈ 4.5 mW.

Fig. 13
Fig. 13

Calculated (solid line) and measured carrier levels as a function of read (= bias) power level. RE–TM thin film on an ungrooved glass substrate, scanning velocity = 5.5 m/s, and applied field = 300 Oe. Calculated values normalized to the measured value at 1.95-mW bias power level for comparative purposes.

Fig. 14
Fig. 14

Numerically evaluated values of the integral in expression (A5) as a function of 2β2W(Wx′) compared with its approximation, expression (A6).

Fig. 15
Fig. 15

Measured mark length error (in nanoseconds) vs [1 −(ORPrPb)/(PPb)] for various media velocities. RE–TM thin film on an ungrooved glass substrate. Bias power = 2 mW, write pulse length = 2.5 μm, and applied field = 300 Oe.

Fig. 16
Fig. 16

Slopes of power series (in nanoseconds calculated from the data in Fig. 13) vs the inverse of the scanning velocity (in m/s). RE–TM thin film on an ungrooved glass substrate. Bias power = 2 mW, write pulse length = 2.5 μm, and applied field = 300 Oe.

Equations (52)

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m = tanh ( m / t ) ,
T ( x , y ) = A P b exp ( - β 2 y 2 ) - 0 exp [ - β 2 ( x - v t ) 2 ] d t + A P w exp ( - β 2 y 2 ) τ exp [ - β 2 ( x - v t ) 2 ] d t + A P b exp ( - β 2 y 2 ) τ exp [ - β 2 ( x - v t ) 2 ] d t = A P b exp ( - β 2 y 2 ) - exp [ - β 2 ( x - v t ) 2 d t + A ( P w - P b ) exp ( - β 2 y 2 ) 0 τ exp [ - β 2 ( x - v t ) 2 ] d t
A = β 2 ( 1 - R ) [ 1 - exp ( - α δ ) ] π δ ρ c ,
T ( x , y ) = A π exp ( - β 2 y 2 ) β v ( P b + 1 2 ( P w - P b ) × { erf ( β x ) + erf [ β ( L - x ) ] } ) .
T th = A π β v { [ 1 - erf ( β L / 2 ) ] P b + erf ( β L / 2 ) P th , }
P th = 1 erf ( β L / 2 ) { β v T th A π - [ 1 - erf ( β L / 2 ) ] P b }
ORP w = ( β v T th A π - P b ) 2 erf ( β L ) + P b ,
ORP w = 2 erf ( β L / 2 ) erf ( β L ) ( P th - P b ) + P b .
ORP w 2 P th - P b .
L = 10 6 π β erf ( β L ) 1 - exp ( - β 2 L 2 ) [ 1 - ( ORP w - P b P w - P b ) ] ( μ m ) .
TIA = 10 9 π β v erf ( β L ) 1 - exp ( - β 2 L 2 ) [ 1 - ( ORP w - P b P w - P b ) ] ( ns ) .
0.5 eff π β [ 1 - ( ORP w - P b ORP r - P b ) ] .
ORP w - P b ORP r - P b ( 1 - 1 2 2 π ) 0.80.
ORP r 1.25 ORP w - 0.25 P b 2.5 P th - 1.5 P b .
I * erf ( β w ) { erf [ β ( L m 2 - ) ] + erf [ β ( L l 2 + ) ] - 1 } .
β w { ln [ P b + ( P w - P b ) erf ( β L m / 2 ) P b + ( P th - P b ) erf ( β L m / 2 ) ] } 1 / 2 .
β w [ ln ( P w P th ) ] 1 / 2 .
β w [ ln ( 2.5 P th - 1.5 P b P th ) ] 1 / 2 .
w ORP 2 σ eff ( ln 2.5 ) 1 / 2 1.354 σ eff .
I 50 % * erf ( β w ) { 2 × erf [ β ( L 2 ) ] - 1 } .
I isolated * erf ( β w ) × erf [ β ( L m 2 - ) ] .
( P w TIA ) P u = ORP r 0.32 × 10 3 v ( P th - P b ) ( ns / mW ) .
ORP r 2.1 P th - 1.17 P b ,
θ k * 1.16 1 - t 2 ,
t 273 + T amb T c + T th T c exp { - β 2 [ ( x - L / 2 ) 2 + y 2 ] } × [ P r erf ( β L / 2 ) P b + ( P th - p b ) erf ( β L / 2 ) ] ,
t 273 + T amb T c + P r T th P th T c exp { - β 2 [ ( x - L / 2 ) 2 + y 2 ] } .
I max * P r 0 L 0 w exp { - β 2 [ ( x - L / 2 ) 2 + y 2 } θ k * ( x , y ) d x d y .
C 20 log 10 ( I max * ) .
I ( x ) 0 W erf { β Y ( x ) } exp [ - β 2 ( x - x ) 2 ] d x + erf { β W } w exp [ - β 2 ( x - x ) 2 ] d x ,
I x - 0 W erf { β Y ( x ) } x { exp [ - β 2 ( x - x ) 2 ] } d x + erf { β W } W x { exp [ - β 2 ( x - x ) 2 ] } d x = - { erf { β Y } exp [ - β 2 ( x - x ) 2 ] } W 0 + 0 W exp [ - β 2 ( x - x ) 2 ] exp [ - β 2 Y 2 ) Y x d x - erf { β W } { exp [ - β 2 ( x - x ) 2 ] } W .
I x - erf { β W } exp [ - β 2 ( W - x ) 2 ] + erf { β W } exp [ - β 2 ( W - x ) 2 ] + 0 W exp { - β 2 [ ( x - x ) 2 + Y 2 ] } d Y .
I x 0 W exp ( - β 2 { [ ( W - x ) - W 2 - Y 2 ] 2 + Y 2 } ) d Y .
I x exp { - β 2 [ ( W - x ) 2 + W 2 ] } × 0 π 2 exp [ 2 β 2 W ( W - x ) cos θ ] cos θ d θ .
I ° exp [ 1.634 β 2 W ( W - x ) ]
I x exp { - β 2 [ ( W - x ) 2 + W 2 ] } × [ 1 + ( 0.785 a ) 1 ! + ( 0.817 a ) 2 2 ! + ( 0.838 a ) 3 3 ! + ] ,
I x exp { - β 2 [ ( W - x ) 2 + W 2 - 1.634 W ( W - x ) ] } .
2 I x 2 = 0 = - β 2 [ - 2 ( W - x ) + 1.634 W ] × exp { - β 2 [ ( W - x ) 2 + W 2 - 1.634 W ( W - x ) ] } .
[ - 2 ( W - x ) + 1.634 W ] 0.
x = 0.183 W .
= 2 × 0.183 W = 0.183 FWHM 0.43 σ eff ,
TIA * = TIA - 10 9 v ( ns ) .
TIA * = 10 9 π β v erf ( β L ) exp ( - β 2 L 2 ) × [ 1 - ( ORP w - P b P w - P b ) ] - 10 9 v ( ns ) .
TIA * 10 9 π β v [ 1 - ( ORP w - P b P w - P b ) ] - 10 9 v ( ns ) .
π β [ 1 - ( ORP w - P b ORP r - P b ) ] ( m ) .
( ORP w - P b ) = ( ORP r - P b ) ( 1 - β π ) ( mW ) .
TIA * 10 9 π β v [ 1 - ( ORP r - P b P w - P b ) { 1 - β π } ] - 10 9 v ( ns ) = 10 9 π β v [ 1 - ( ORP r - P b P w - P b ) { 1 - β π } ] - β π ( ns ) .
TIA * = 10 9 π β v ( 1 - β π ) [ 1 - ( ORP r - P b P w - P b ) ] ( ns ) .
10 9 π β ( 1 - β 10 9 π ) 927.5.
10 9 σ eff ( 2 π - K ) 927.5 ,
k ( 2 π - 927.5 10 9 σ eff ) .
[ L phys - L det ] 0.233 σ eff .
TIA * = 10 9 σ eff v ( 2 π - k ) [ 1 - ( ORP r - P b P w - P b ) ] ( ns ) .

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