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Considerations of eye-safety in intense diffuse illumination
Volume
12, number
1
CONSIDERATIONS
OPTICS COMMUNICATIONS
OF EYE-SAFETY
September
IN INTENSE
DIFFUSE
1974
ILLUMINATION
1.N. ROSS Natiorlal Physical
Laboratory,
Received
I July
Teddington,
Middx.,
UK
1974
The probability of marginal damage to one receptor of the retina is calculated for the case of coherent diffuse illumination of the eye. The effect of ‘speckle’ is estimated and the illumination is not restricted to that from a lambertian diffuser. An arrangement employing a ruby laser illuminator, which has been used for holography, is assessed and shown to be “safe” in terms of the present Codes of Practice.
1. Introduction Applications of pulsed laser holography include the recording of human subjects both for display purposes and to obtain medical information. In such a process the expansion of the laser beam to illuminate the whole of the subject may be carried out either by diverging the beam with lenses or mirrors, in which case a near spherical wave strikes the subject, or by scattering the light at a diffuser. In the case of direct or specularly reflected illumination the consideration of the possible hazard to the subject’s eyes may be based on the limits suggested by the various safety codes [ 1,2]. The code which appears to be currently accepted in the UK and which recommends the strictest limits is that produced by the British Standards Institution [l] In most practical situations, the conclusion reached by applying the limits in this code is that one cannot use this type of illumination unless it is absolutely certain that no energy can reach the pupil by a direct path. For diffuse illumination, however, the limits set by the code may be interpreted in various ways some of which result in unnecessary restriction and it is the purpose of this note to suggest a method of calculating, for the case of diffuse illumination, whether or not a particular illumination is hazardous to the eye. The most basic and useful reference limit given in the safety code is the ‘maximum permissible energy density falling on the retina’. The alternative limit given 46
is the ‘maximum permissible energy density falling on the cornea’ but when the light is even slightly diffused this limit implies an overestimated and therefore unnecessarily restricting ‘concentration factor’ for the eye.
2. Calculation Consider an eye exposed to a laser beam via a diffuser at which all the radiation is diffused, but not necessarily uniformly (fig. 1). The assessment of the hazard will be considered as follows: 1. Calculation of the mean retinal energy density in terms of an easily measurable quantity. By choosing to measure the energy density incident at the eye (EE), the scattering and attenuating properties of the diffuser are taken into account. 2. Calculation of the variation of the retinal energy density with distance (15) of the eye from the diffuser. This enables the value at the worst position to be deduced from a measurement at an arbitrary eye position. 3. The illumination on the retina is subject to random spatial variations of intensity (known as ‘speckle’) as a result of the coherent nature of the light and therefore contains intensities both well above and well below the mean. In the presence of speckle one must take account of the probability of finding, somewhere on the retina, an energy density greater than the
Volume
12, number
1
OPTICS
COMMUNICATIONS
September
Diffuser
1974
Eye
Fig. 1. Diffuse illumination of the retina, with the eye focussed on the diffuser. ED = Energy energy per unit area incident on the eye, ER = energy per unit area incident on the retina.
maximum permissible level. This chance is still appreciable, as pointed out by Burch and Gates [3], when the mean energy density is a small fraction of the maximum permissible energy density. 4. The calculation of subsection 2.3 assumes complete coherence of radiation forming the speckle pattern. The effect of reducing the coherence will also be considered. 2.1. Calculation of mean retinal energy density Using the symbols of fig. 1: The energy entering eye = EE X pupil area = EE * anb2 The image area on retina = diffuser area X cf/,5)2
per unit area leaving diffuser,
(f= 17 mm) and the maximum eq. (1) gives:
EE =
pupil size (b = 7 mm),
ER = 26.0 J/m2. This is less than the maximum permissible level laid down in the code by a factor 6.2. 2.2. Variation of ER with distance from the diffuser Fig. 2 indicates the geometry, with the eye focussed to a distance L’. Let energy leaving small area dS on diffuser into solid angle dSZ be EO d,S da F(0), where E, is a constant and F(0) is the scattering function of the diffuser. .’. Energy entering eye from dS
= $7~0~ (f/L)2 , .’. The mean retinal energy density, ER =
(1)
A practical example illustrates the calculation. In recent experiments in recording holograms of human subjects, the beam illuminating the subject was derived from a Q-switched ruby laser (Barr and Stroud: LU6), diverged through a diffuser (Kodatrace). A small aperture (D = 12.7 mm) was placed at the brightest part of the diffuser and the energy density EE, in the region of the subjects eye at a distance L = 455 mm from the diffuser, was measured to be 120 mJ/m2 using a holographic exposure meter (Robin Ltd: Model 7490). Assuming the usual values for the focal length of the eye
where we integrate over the eye pupil. Area S of diffuser contributing to the illumination of dA = NC+Lwql 2, where B = area of eye pupil. Thus L,-L (j&s= [ Ll
1 2
aB
(3)
The solid angle dCl at the diffuser giving a spot size d.4 on the retina is given, on application of the lens formula, by : 2dA F’
(4)
.’. From (2) using (3) and (4): Eo i& = - j-F(B) dB , f:
(5) 47
Volume
I
12, number
OPTICS COMMUNICATIONS
September
Diffuser
Fig. 2. Diffuse
illumination
1974
Eye
of the retina,
with the eye focussed
where 8 is a function of position in the pupil. The maximum variation of 0 over the pupil is
to an arbitrary
distance
L1.
He also showed [S] that, for the average of m independent trials:
(b/L, )ma. = 71250 = 0.028 rad = l”36’ , (7) where the pupil diameter is taken to be 7 mm and the minimum focussing distance to be 250 mm. In practice, for all diffusers likely to be used, F(0) can be regarded as constant over this range of 0 at the angle at which its value is a maximum (most dangerous position for the eye). Thus, eq. (5) approximates to: 2 F(Q)
7
where BE is the value of 0 at the eye. It can be seen that the retinal energy density is independent of the distance from the diffuser and a measurement at one distance is valid for all other distances. 2.3. Probability of finding an energy density greater than the maximum permissible level
This equation applies in two situations relevant to the problem being considered: i) It gives the probability of finding a particular energy density in a speckle pattern formed from m independent modes of the laser. It is thus possible to assess the effect of partial coherence. ii) It also gives the probability of measuring a particular intensity when the detector aperture is averaging over an appreciable area in the speckle pattern. The value taken by m (the number of independent elements in the detector aperture) was computed by Goodman [6] for the case of a detector aperture (size a) looking, from a distance f,at a uniformly and diffusely illuminated aperture (size b). A good approximation to his computed values of m, for m > 1.5 is given by: m=19N2+1,
(8)
where the Fresnel number, N, is given by Rayleigh [4] showed that in a speckle pattern, formed from a perfectly coherent source, the probability of finding an energy density between E and E + dE is given by: p(x) dx = ecx dx ,
(6)
where X=
48
energy density mean energy density
E E’
N,ab 4V. To calculate m for the eye it is necessary to ascertain what is the size of the effective ‘detector aperture’ of the retina. As a result of factors such as the discrete receptor structure of the retina and the finite time required to generate eye damage coupled with the rapid diffusion of heat away from a small illuminated spot, the parameter determining the damage threshold in-
Volume 12, number 1
OPTICS COMMUNICATIONS
volves a spatial integration of the retinal illumination. As an approximation we can consider the retina to be an array of ‘unit cells’, each cell responding to the average illumination over the cell, and each cell operating independently of its neighbours. This ‘unit cell’ is therefore the ‘detector aperture’ of the retina. There is insufficient evidence to calculate the size of the unit cell and we assume it to be 5 pm, this being the size of the retinal receptor and also the minimum size of the mean speckle size on the retina that can just be perceived. Using this value (a = 5 pm), the Fresnel number of the eye is calculated to be 0.74 where X = 0.694 pm (ruby laser wavelength). Thus, using eq. (8):
September 1974
(11) P(>x,) can now be evaluated if we assign the appropriate value to M, the number of illuminated unit cells on the retina. Now, since illuminated area on retina = irrD2(f/L)2 (see fig. 1) M=-
m=19N2+1=11.4. We can now calculate from eq. (7) the probability of any one cell having a particular (average) energy density. The parameter we wish to calculate however is the chance of one or more cells on the retina having more than the maximum permissible level. If the retina is illuminated uniformly (apart from speckle effects) over a region containingM unit cells, the probability of those M cells having energy densities between x1 and x1 + dxl, x2 and x2 + dx2, . .. . xM and xM + dxM, respectively is:
illuminated area on retina Df area of unit cell aL -i-l
2
(IV
As an example, which closely approximates our previous example, we choose x0 = 6 and m = 11. Also, using eq. (12): M = 1.6 X 105. Inserting these values into eq. (11) and evaluating gives: P(>6)
= 1.8 X lo-l3
.
and, the probability of at least one cell having an energy density greater than x0 [say P(>xo)] is:
Thus there is a negligible probability of exceeding the maximum permissible energy density on the retina. Alternatively we can calculate the maximum mean retinal energy that can be regarded as safe. Let maximum permissible P(>x,) = 1Op3. Inserting this value and the values for m and M into eq. (11) enables a calculation of the minimum permissible x0. This calculation gives:
P(>x,)
minimum
pm (XI) k,
- 7 7 00
d.9 .... pm GM) d+z 1
= 1
. .. 7 0
Substituting P(>x,)
P,,, (4
pm (XI> dx, p,n (~2) dx,... pm (x,d~~
for p,,,(x) from eq. (7) and integrating:
= 1-
[1
mcl(mxo)k
1 - eemxe k=O 7
In most cases the Poisson approximation
P(>x,) Or, if
= 1 -exp
[(
1. JV
(9)
is valid:
. )I00)
mgl (mxo)k i14e-mxek=0 r
x0 = 3.6 ,
i.e. since the maximum permissible energy density on the retina = 160 J/m2, then the mean energy density of diffuse illumination of the retina must not exceed 160/3.6 = 45 J/m2. For the case represented in the earlier example this indicates that the energy density falling on the eye must be less than 200 mJ/m2. (measured value was 120 mJ/m2 .) A safety factor of 10 is included in the safety codes and more than adequately covers the effects of speckle, but without being sure that the safety factor is intended for this purpose we have assumed that it is not. In spite of this we have shown that a typical system using diffuse illumination is well within the existing codes of practice.
49
Volume
12, number
1
2.4. Effect of coherence
OPTICS COMMUNICATIONS
on speckle
We have assumed that the speckle illumination of the retina is formed from a perfectly coherent source. All rays arriving at a given point on the retina must be coherent. For the eye focussed onto the diffuser this is the case if the coherence is high over an area of the diffuser determined by the resolution limit of the eye. Thus our analysis is valid if there is high coherence over a circle of radius r on the diffuser where Y= La and (Y= angular resolution limit of the eye. For example, let cy= 1 min and L = 500 mm . r=O.lSmm=
150pm.
If the diffuser is directly illuminated by the expanded laser beam the coherence will almost certainly be high over a larger radius than this. If this is so our analysis is valid. If the coherence range is less than this or if the eye is not focussed on the diffuser (and the required coherence range becomes greater than that present) the speckle becomes less contrasty and there is even less chance of energy densities considerably higher than the mean. Thus the risk of eye damage in these cases is even less than the risk which has been assessed above.
3. Conclusions We have calculated, from an easily measurable quantity, the chances of exceeding the maximum permis-
50
September
1974
sible energy density on one receptor of the retina when using coherent diffuse illumination. An example showed that the holographic recording of human subjects can be free of eye-hazard even under the assumption that the codes do not include the effects of speckle in their safety factor. Also, in many situations the risk is even less than that obtained using the calculation presented in this note.
Acknowledgement
The author wishes to express thanks to Dr. J.W.C. Gates and Mr. R.G.N. Hall for their contributions to the substance and presentation of this note, and to Dr. J.M. Burch, with whom he had several fruitful discussions.
References [ I] Protection of Personnel against Hazards of Laser Radiation: British Standards Institution: BS 4803: 1972. [ 21 American National Standard for the Safe Use of Lasers: American National Standards Institution: ANSI: Z 136: 1 -. 1973. [3] J.M. Burch and J.W.C. Gates, Ann. Occup. Hyg. Suppl. (1967) 65. [4] Lord Rayleigh, Phil. Mag. 10 (1880) 73. [5] Lord Rayleigh, Phil Mag. 36 (1918) 429. [6] J.W. Goodman, Proc. IEEE 53 (1965) 1688.
12, number
1
CONSIDERATIONS
OPTICS COMMUNICATIONS
OF EYE-SAFETY
September
IN INTENSE
DIFFUSE
1974
ILLUMINATION
1.N. ROSS Natiorlal Physical
Laboratory,
Received
I July
Teddington,
Middx.,
UK
1974
The probability of marginal damage to one receptor of the retina is calculated for the case of coherent diffuse illumination of the eye. The effect of ‘speckle’ is estimated and the illumination is not restricted to that from a lambertian diffuser. An arrangement employing a ruby laser illuminator, which has been used for holography, is assessed and shown to be “safe” in terms of the present Codes of Practice.
1. Introduction Applications of pulsed laser holography include the recording of human subjects both for display purposes and to obtain medical information. In such a process the expansion of the laser beam to illuminate the whole of the subject may be carried out either by diverging the beam with lenses or mirrors, in which case a near spherical wave strikes the subject, or by scattering the light at a diffuser. In the case of direct or specularly reflected illumination the consideration of the possible hazard to the subject’s eyes may be based on the limits suggested by the various safety codes [ 1,2]. The code which appears to be currently accepted in the UK and which recommends the strictest limits is that produced by the British Standards Institution [l] In most practical situations, the conclusion reached by applying the limits in this code is that one cannot use this type of illumination unless it is absolutely certain that no energy can reach the pupil by a direct path. For diffuse illumination, however, the limits set by the code may be interpreted in various ways some of which result in unnecessary restriction and it is the purpose of this note to suggest a method of calculating, for the case of diffuse illumination, whether or not a particular illumination is hazardous to the eye. The most basic and useful reference limit given in the safety code is the ‘maximum permissible energy density falling on the retina’. The alternative limit given 46
is the ‘maximum permissible energy density falling on the cornea’ but when the light is even slightly diffused this limit implies an overestimated and therefore unnecessarily restricting ‘concentration factor’ for the eye.
2. Calculation Consider an eye exposed to a laser beam via a diffuser at which all the radiation is diffused, but not necessarily uniformly (fig. 1). The assessment of the hazard will be considered as follows: 1. Calculation of the mean retinal energy density in terms of an easily measurable quantity. By choosing to measure the energy density incident at the eye (EE), the scattering and attenuating properties of the diffuser are taken into account. 2. Calculation of the variation of the retinal energy density with distance (15) of the eye from the diffuser. This enables the value at the worst position to be deduced from a measurement at an arbitrary eye position. 3. The illumination on the retina is subject to random spatial variations of intensity (known as ‘speckle’) as a result of the coherent nature of the light and therefore contains intensities both well above and well below the mean. In the presence of speckle one must take account of the probability of finding, somewhere on the retina, an energy density greater than the
Volume
12, number
1
OPTICS
COMMUNICATIONS
September
Diffuser
1974
Eye
Fig. 1. Diffuse illumination of the retina, with the eye focussed on the diffuser. ED = Energy energy per unit area incident on the eye, ER = energy per unit area incident on the retina.
maximum permissible level. This chance is still appreciable, as pointed out by Burch and Gates [3], when the mean energy density is a small fraction of the maximum permissible energy density. 4. The calculation of subsection 2.3 assumes complete coherence of radiation forming the speckle pattern. The effect of reducing the coherence will also be considered. 2.1. Calculation of mean retinal energy density Using the symbols of fig. 1: The energy entering eye = EE X pupil area = EE * anb2 The image area on retina = diffuser area X cf/,5)2
per unit area leaving diffuser,
(f= 17 mm) and the maximum eq. (1) gives:
EE =
pupil size (b = 7 mm),
ER = 26.0 J/m2. This is less than the maximum permissible level laid down in the code by a factor 6.2. 2.2. Variation of ER with distance from the diffuser Fig. 2 indicates the geometry, with the eye focussed to a distance L’. Let energy leaving small area dS on diffuser into solid angle dSZ be EO d,S da F(0), where E, is a constant and F(0) is the scattering function of the diffuser. .’. Energy entering eye from dS
= $7~0~ (f/L)2 , .’. The mean retinal energy density, ER =
(1)
A practical example illustrates the calculation. In recent experiments in recording holograms of human subjects, the beam illuminating the subject was derived from a Q-switched ruby laser (Barr and Stroud: LU6), diverged through a diffuser (Kodatrace). A small aperture (D = 12.7 mm) was placed at the brightest part of the diffuser and the energy density EE, in the region of the subjects eye at a distance L = 455 mm from the diffuser, was measured to be 120 mJ/m2 using a holographic exposure meter (Robin Ltd: Model 7490). Assuming the usual values for the focal length of the eye
where we integrate over the eye pupil. Area S of diffuser contributing to the illumination of dA = NC+Lwql 2, where B = area of eye pupil. Thus L,-L (j&s= [ Ll
1 2
aB
(3)
The solid angle dCl at the diffuser giving a spot size d.4 on the retina is given, on application of the lens formula, by : 2dA F’
(4)
.’. From (2) using (3) and (4): Eo i& = - j-F(B) dB , f:
(5) 47
Volume
I
12, number
OPTICS COMMUNICATIONS
September
Diffuser
Fig. 2. Diffuse
illumination
1974
Eye
of the retina,
with the eye focussed
where 8 is a function of position in the pupil. The maximum variation of 0 over the pupil is
to an arbitrary
distance
L1.
He also showed [S] that, for the average of m independent trials:
(b/L, )ma. = 71250 = 0.028 rad = l”36’ , (7) where the pupil diameter is taken to be 7 mm and the minimum focussing distance to be 250 mm. In practice, for all diffusers likely to be used, F(0) can be regarded as constant over this range of 0 at the angle at which its value is a maximum (most dangerous position for the eye). Thus, eq. (5) approximates to: 2 F(Q)
7
where BE is the value of 0 at the eye. It can be seen that the retinal energy density is independent of the distance from the diffuser and a measurement at one distance is valid for all other distances. 2.3. Probability of finding an energy density greater than the maximum permissible level
This equation applies in two situations relevant to the problem being considered: i) It gives the probability of finding a particular energy density in a speckle pattern formed from m independent modes of the laser. It is thus possible to assess the effect of partial coherence. ii) It also gives the probability of measuring a particular intensity when the detector aperture is averaging over an appreciable area in the speckle pattern. The value taken by m (the number of independent elements in the detector aperture) was computed by Goodman [6] for the case of a detector aperture (size a) looking, from a distance f,at a uniformly and diffusely illuminated aperture (size b). A good approximation to his computed values of m, for m > 1.5 is given by: m=19N2+1,
(8)
where the Fresnel number, N, is given by Rayleigh [4] showed that in a speckle pattern, formed from a perfectly coherent source, the probability of finding an energy density between E and E + dE is given by: p(x) dx = ecx dx ,
(6)
where X=
48
energy density mean energy density
E E’
N,ab 4V. To calculate m for the eye it is necessary to ascertain what is the size of the effective ‘detector aperture’ of the retina. As a result of factors such as the discrete receptor structure of the retina and the finite time required to generate eye damage coupled with the rapid diffusion of heat away from a small illuminated spot, the parameter determining the damage threshold in-
Volume 12, number 1
OPTICS COMMUNICATIONS
volves a spatial integration of the retinal illumination. As an approximation we can consider the retina to be an array of ‘unit cells’, each cell responding to the average illumination over the cell, and each cell operating independently of its neighbours. This ‘unit cell’ is therefore the ‘detector aperture’ of the retina. There is insufficient evidence to calculate the size of the unit cell and we assume it to be 5 pm, this being the size of the retinal receptor and also the minimum size of the mean speckle size on the retina that can just be perceived. Using this value (a = 5 pm), the Fresnel number of the eye is calculated to be 0.74 where X = 0.694 pm (ruby laser wavelength). Thus, using eq. (8):
September 1974
(11) P(>x,) can now be evaluated if we assign the appropriate value to M, the number of illuminated unit cells on the retina. Now, since illuminated area on retina = irrD2(f/L)2 (see fig. 1) M=-
m=19N2+1=11.4. We can now calculate from eq. (7) the probability of any one cell having a particular (average) energy density. The parameter we wish to calculate however is the chance of one or more cells on the retina having more than the maximum permissible level. If the retina is illuminated uniformly (apart from speckle effects) over a region containingM unit cells, the probability of those M cells having energy densities between x1 and x1 + dxl, x2 and x2 + dx2, . .. . xM and xM + dxM, respectively is:
illuminated area on retina Df area of unit cell aL -i-l
2
(IV
As an example, which closely approximates our previous example, we choose x0 = 6 and m = 11. Also, using eq. (12): M = 1.6 X 105. Inserting these values into eq. (11) and evaluating gives: P(>6)
= 1.8 X lo-l3
.
and, the probability of at least one cell having an energy density greater than x0 [say P(>xo)] is:
Thus there is a negligible probability of exceeding the maximum permissible energy density on the retina. Alternatively we can calculate the maximum mean retinal energy that can be regarded as safe. Let maximum permissible P(>x,) = 1Op3. Inserting this value and the values for m and M into eq. (11) enables a calculation of the minimum permissible x0. This calculation gives:
P(>x,)
minimum
pm (XI) k,
- 7 7 00
d.9 .... pm GM) d+z 1
= 1
. .. 7 0
Substituting P(>x,)
P,,, (4
pm (XI> dx, p,n (~2) dx,... pm (x,d~~
for p,,,(x) from eq. (7) and integrating:
= 1-
[1
mcl(mxo)k
1 - eemxe k=O 7
In most cases the Poisson approximation
P(>x,) Or, if
= 1 -exp
[(
1. JV
(9)
is valid:
. )I00)
mgl (mxo)k i14e-mxek=0 r
x0 = 3.6 ,
i.e. since the maximum permissible energy density on the retina = 160 J/m2, then the mean energy density of diffuse illumination of the retina must not exceed 160/3.6 = 45 J/m2. For the case represented in the earlier example this indicates that the energy density falling on the eye must be less than 200 mJ/m2. (measured value was 120 mJ/m2 .) A safety factor of 10 is included in the safety codes and more than adequately covers the effects of speckle, but without being sure that the safety factor is intended for this purpose we have assumed that it is not. In spite of this we have shown that a typical system using diffuse illumination is well within the existing codes of practice.
49
Volume
12, number
1
2.4. Effect of coherence
OPTICS COMMUNICATIONS
on speckle
We have assumed that the speckle illumination of the retina is formed from a perfectly coherent source. All rays arriving at a given point on the retina must be coherent. For the eye focussed onto the diffuser this is the case if the coherence is high over an area of the diffuser determined by the resolution limit of the eye. Thus our analysis is valid if there is high coherence over a circle of radius r on the diffuser where Y= La and (Y= angular resolution limit of the eye. For example, let cy= 1 min and L = 500 mm . r=O.lSmm=
150pm.
If the diffuser is directly illuminated by the expanded laser beam the coherence will almost certainly be high over a larger radius than this. If this is so our analysis is valid. If the coherence range is less than this or if the eye is not focussed on the diffuser (and the required coherence range becomes greater than that present) the speckle becomes less contrasty and there is even less chance of energy densities considerably higher than the mean. Thus the risk of eye damage in these cases is even less than the risk which has been assessed above.
3. Conclusions We have calculated, from an easily measurable quantity, the chances of exceeding the maximum permis-
50
September
1974
sible energy density on one receptor of the retina when using coherent diffuse illumination. An example showed that the holographic recording of human subjects can be free of eye-hazard even under the assumption that the codes do not include the effects of speckle in their safety factor. Also, in many situations the risk is even less than that obtained using the calculation presented in this note.
Acknowledgement
The author wishes to express thanks to Dr. J.W.C. Gates and Mr. R.G.N. Hall for their contributions to the substance and presentation of this note, and to Dr. J.M. Burch, with whom he had several fruitful discussions.
References [ I] Protection of Personnel against Hazards of Laser Radiation: British Standards Institution: BS 4803: 1972. [ 21 American National Standard for the Safe Use of Lasers: American National Standards Institution: ANSI: Z 136: 1 -. 1973. [3] J.M. Burch and J.W.C. Gates, Ann. Occup. Hyg. Suppl. (1967) 65. [4] Lord Rayleigh, Phil. Mag. 10 (1880) 73. [5] Lord Rayleigh, Phil Mag. 36 (1918) 429. [6] J.W. Goodman, Proc. IEEE 53 (1965) 1688.