Int. J. Impact Engng Vol. 14, pp .49-60 , 1993 0734-743X/93 $6.00+0.00 Printed in Great Britain © 1993 Pergamon Press Ltd

I M P A C T D A M A G E A N D O P T I C A L S C A T T E R

Dale Atkinson & Alan Watts

POD Associates, Inc., 2309 Renard Place, NE, Suite 201, Albuquerque, NM 87106

ABSTRACT

Much recent data from the Long Duration Exposure Facility (LDEF) have confirmed that for multiyear periods in LEO many satellite surfaces (especially the RAM) will be subjected to significant bombardment by small particles in the 1 to 100 micron size domain. These particles are both mierometeoroids and man-made debris. Of interest is the consequential effects on precision surfaces such as high-resolution optics. The damage produced does not necessarily seriously downgrade the reflectivity (for mirrors) or transmissivi~ (for lenses), but can significantly worsen optical scatter. Since many optics are not simple metal mirrors, for which the major response is near-hemispherical cratering, but frequently comprise brittle dielectrics (including multilayer coatings) which suffer conchoidal cratering, star cracking and interlayer differential delamination, the correlation between the induced mechanical damage and the resulting optical scatter is complex. An approach is given which attempts to analytically predict the material damage modes for various impact conditions, and also correlate this damage with optical scatter.

INTRODUCTION

With man's ever increasing activity in space an issue has arisen concerning the problem of impacts on space assets due to either the naturally occurring micrometeoroids or man-made debris. Both species of particles cover a large range of sizes, from sub-micron to many centimeters, and for each species the relative number of particles rapidly increases with decreasing particle size. The micrometeoroids approach the earth from all directions with a mean collision speed of about 20 km/s (ranging from a low of a few km/s to a high of about 79 kin/s). These particles undergo a one-shot pass of the earth, since they are in orbit around the sun. The mean density of micrometeoroids is about 0.5 g/cm j, although there is a small component of higher density asteroidal matter (8.0 g/cm3). The man-made debris is assumed to be mostly in pseudo-circular orbits about the earth, with a mean collision speed of about I0 km/s (range from about zero for similar orbits to almost 16 km/s for counter orbits). The debris is primarily aluminum, but also comprises alumina (fuel pellets) and high density remnants of damaged satellites, rocket boosters, sundry bolts and lens caps, etc.. Full details of the mierometeoroid and debris models are given in Cour-Palais (1969) and Kessler (1988), respectively.

Historically much emphasis has been given to the problem of catastrophic collisions due to the larger particles (> 1.0 cm diameter) with satellites. However, these large particles constitute a relatively low flux (,potential hits per m 2 per unit time), and much of the analysis is concentrated on the Poissonian

49

50 D AIKINSO'x ~lld A, WAl l s

probability of impacts occurring on a given body. More recently attention is being devoted to the problems associated with the much higher flux of the small particles (especially in the 1 to 100 micron range). These latter can cause surface erosions of critical components such as optical surfaces.

This paper addresses the issue of surface erosion of optical components, and considers the nature of the impact damage and the first-order estimates of induced optical scatter. The studies are of interest to the hypervelocity impact community since they involve the problems of fragmentation, cratering and cracking logic, in addition to the estimates of optical scatter.

In order to assess impact damage we have incorporated the existing micrometeoroid and debris models into a computer program called SPENV. This code allows predictions of the expected impact fluences (hits per area) as functions of: satellite time on orbit, orbital inclination, altitude and the direction of a given surface of the satellite relative to the velocity vector (e.g. RAM, SPACE, EARTH, SIDES and TRAIL). The code has been benehmarked versus the recent LDEF data, giving agreement to better than a factor of three. LDEF was at an altitude of 475 km, with inclination of 28.5 degrees, and flew for 5.75 years. A large amount of impact data is steadily being gleaned from this experiment including cratering, perforations, and delaminations and star-cracking in brittle materials.

In order to more accurately determine the responses for altitudes near and above 1000 km, it is necessary to modify the Kessler model for orbital debris. This modification has been incorporated into the SPENV computer program using the ratio of US Space Command data versus the normal Kessler model. The underlying assumption for this modification is that the small debris distribution tends to follow that of the larger (> 10 cm), trackable, debris. This assumption has been borne out by the LDEF data at 500 km, and is assumed for the higher altitudes.

FRAGMENTATION

When bodies undergo hypervelocity impacts it is experimentally observed that the fragments usually display a power-law (i.e. fractal) distribution for the remnants of the form:

N(>m) = or(M/m) 13 (1)

where N is the cumulative number of fragments of mass m or greater, M is the original total mass, and cL and 13 are constant coefficients. Typically, the experimental value of 13 is about 0.75. Assuming constant density and spherical particles the distribution becomes:

N(>d) = cx(D/d) 313 (2)

where D is the initial body diameter, and d is the fragment diameter. Thus 313 = 2.25. This value is very close to the suggested index value of 2.5 used in the Kessler debris model to describe the small (<1 cm) particle distribution.

Assuming the power law applies from the largest remnant to very small ones, then in order to conserve total mass we require:

(1/o0 = (13/(1-13)) ~ which implies m(1) = M (1/cx) "''~ (3)

Thus for 13= 0.75 we have o~ = 0.4387 and m(1) = 0.3334 M (or d(1) = 0.693 D) for the largest remaining fragment. To fit the Kessler model (i.e. 313 = 2.5) we require cz = 0.2615, and m(1) = 0.2 M (or d(1) = 0.585 D). It should be noted that the Kessler model is primarily based on an interpolation between small particle (< 10 micron) perforations observed on satellites (including Solar Max) and the radar-observable larger particles (> 5 cm), although the LDEF data is presently in agreement with the model to within the accuracies of interpretation. This fact suggests that a significant portion of the small particle population is itself caused by continual collisional fragmentation.

Impact damage and optical scatter 51

CRATERING DATA AND LOGIC

A large portion of the data from LDEF consists of impact craters, especially in the aluminum structure. The particle flux models describe numbers of particles, however. To relate the two it is necessary to invoke a scaling law for cratering. To date the SPENV code has invoked the simplest of the sealing laws, namely the "energy law", which predicts:

dc = const (P /P t ) 'n u2~dp (4)

where d c is the crater diameter, dp is the particle diameter, p refers to the density of particle or target, and u is the impact speed normal to the target surface, while the constant is a normalizer based on experimental impact data of aluminum into aluminum. To date this simple law gives a reasonable fit to the LDEF data in collaboration with the existing micrometeoroid and debris models.

Most other sealing laws (e.g. those by Cour-Palais (1969), McDonnell and Sullivan (1984,1991), etc) are similar to the one above, but frequently differ in the values of the power indices. Changes in the latter will merely linearly shift the "crater count" versus the "particle count" when drawn in the form of cumulative hits per area against size of crater or particle. Since all the scaling laws invoke low indices (< 1) for sensitivities versus density and/or impact speed, the corresponding shifts in the predictions are within the uncertainties of the LDEF data. Supralinearity has been experimentally observed, such that the crater size increases more rapidly than the particle size, all other factors remaining constant. The most widely used superlinear term is in the form of dv L°~ in place of the simple dp term. Use of this term will produce a "skew" to the data, but for such a small non-unity index the shift is well within the uncertainties of the LDEF interpretation.

Another uncertainty is the use of the "cosine rule", which is generally assumed, and which relates cratering only to the component of impact velocity normal to the target surface. For the lower impact speeds the material response is dependent on momentum and thus obeys the cosine rule, at least partially. For the higher impact speeds the response is dependent on energy, and it is by no means clear that the cosine rule applies (surface "explosions" do not depend on direction of arrival). Interestingly, although the particle flux models imply very infrequent normal impacts, the majority of LDEF craters are very close to hemispheres (likewise most of the craters on the moon are also closely hemispherical!). The effect of modifying the cosine rule will also produce a shift in the LDEF interpretation. However, we have not yet investigated this effect.

Fractional Area Damage

To estimate the degree of areal damage we need to know the impact fluences. Figures 1 through 4 give predictions of cumulative impacts per area of surface versus particle size and crater size, for an altitude of 1000 km, orbit inclination of 60 degrees and two satellite surface orientations of RAM and EARTH. The assumed period in orbit is 6 years starting in 1996. To estimate the fractional damage areas we first differentiate the cumulative impact-versus-size function, multiply the function by the corresponding areas of the damage regions (e.g. craters), and then reintegrate.

For example, if the cumulative number (CN) = A / I~ hits per area for particles greater than diameter D, with A a constant, and n the power index, then it can be shown that the corresponding fractional area damage is given by:

Fract ional area = ( x / 4) x k 2 x ( n / ( n - 2 ) ) x A / D *a (5)

where k is the ratio of the crater diameter to the impactor diameter. For the case of small debris (less than 1 cm), n has the value of 2.5 for debris. The above equation can then be rewritten:

Fractional area = (x / 4) x k 2 x 5 x CNt~i~ ) x D,m 2 (6)

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Impact damage and optical scatter 53

1000 km at 60 degree inclination, 1996-2002: EARTH

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The value depends on Dmi , since n is greater than 2. To consider a specific case, we calculate the fractional area of erosion for the RAM surface for the ease of an altitude of 1000 km, and inclination of 60 degrees. For this ease k = 7.0. Assuming that craters of size down to about 1 micron are important (this is comparable to operating wavelengths, and the thicknesses of quarter-wave dielectric optical layers), we obtain:

Fractional area = 7.3 x 10 "4 , i.e. about 0.1 percent.

This is a significant amount of erosion, and can be expected to produce significant optical scatter, as discussed below. Note, however, that the LDEF data has indicated that the Kessler model is tending to over-predict the debris population at the smaller sizes. Consequently, the above estimate is probably too large, by perhaps a factor of three (the error would be much larger if an attempt was made to include sub-micron debris particles). However, the above calculation is only for man-made debris, and the micrometeoroids will also contribute, though to a smaller degree. LDEF itself indicated areal erosions of less than 1 percent for pure cratering, on the thermal control materials facing into the RAM. However, if the damage zone includes other related effects (spalling of paint coats, radial star cracking) then the fractional area affected increases rapidly since these effects increase the value of the k term.

OPTICAL SCATTER FOR CRATERS

The computations of the cumulative hit rate (per square meter) show the impact fluence versus impactor diameters for differing spacecraft surface orientations. These data are augmented with information versus crater sizes. From the latter it is possible to establish first-order estimates of increases in optical scatter. This is done by determining the equivalent "contamination level" as defined in MIL-STD 1246A. Young (1976) has already performed both experiments and computations (using Mie theory) to derive increases in the Bidirectional Reflection Distribution Function (BRDF, per steradian) as functions of contamination levels for small particles on mirror surfaces. Thus by finding the "equivalent" conditions (assuming craters scatter in a similar manner to spheres on a mirror) it is possible to derive the BRDF as functions of wavelength and cratering for any chosen spacecraft surface.

Figure 5 illustrates the MIL-STD 1246A data plotted on the same scales as used for the cumulative impacts (per area) versus crater sizes. Note that each "level" plot curves over as the size decreases (rather like the behavior for mierometeoroids), and that this tendency to asymptote is most obvious for the lower "levels". For reference, note that the meaning of "level" is that the distribution is one for which there is one particle per square foot of surface area (equal to 10.76 per m 2) of size "level" microns diameter (e.g. "200" means there is one particle/ft 2 of diameter 200 microns). The data from Fig. 5 is compared to each of the impact-versus-crater plots, and a mean estimate of equivalent contaminant level is obtained. Clearly, since the two groups of data do not have the same power index, there is no unique solution. However, optical scatter will be dominated by the larger craters, and so the "best" definition of equivalent "level" is found by matching the data at the larger sizes.

As an example, consider the data for the RAM with altitude 1000 km and inclination of 60 degrees. The predictions for debris give about 10.76 impacts/m s for craters of diameter about 0.100 cm (1000 microns), while for mierometeoroids the corresponding size is about 0.06 cm (600 microns). Thus the equivalent MIL-STD levels are about "1000" and "600" for the two particle species. However, the predictions for cratering "slew" across the MIL-STD plots, such that for craters of size 10 microns the corresponding "levels" are about "400" and "100" respectively. Reference to the work of Young, allows BRDF values (near zero degrees off specular) to be estimated. For a working wavelength of 5 microns these are:

For debris BRDF = 10.0 ('level" 1000) to 0.10 ("level" 400) For meteoroids BRDF = 0.78 ("level" 600) to 1.0 x 104 ( 'level" 100)

For the EARTH direction, however, the corresponding crater size is about 250 microns (level "250") with

I m p a c t d a m a g e and op t i ca l sca t ter 55

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56 I). AIKINSON and A. WAr IS

a slew to level "50" for 10 micron craters, and applies only to micrometeoroids (since Kessler's model does not allow impacts on the Earth-facing surface). At 5 micron wavelength the corresponding scatter is:

For meteoroids BRDF = 9.8 x 10 .3 ("level" 250) to 3.1 x 10 "6 ( ' level" 50)

Clearly, the RAM surface suffers from far more scatter than does the EARTH surface.

Scrutiny o f Young's data reveals that his results can be approximately fitted by:

BRDF = 2.5 x 10 "'s x (level) 5 / L 2 (7)

for near-specular scatter, with the wavelength in microns. Note the rapid escalation in the scatter as the "level" increases.

An alternative approach to estimating the scatter is as follows. The fundamental relationship for scatter from craters (assumed the same as from spheres) is:

BRDF = rc 2 x D 4 x N / 1 6 g 2 (8)

where D is the crater diameter, N is the number o f craters per unit area, and ~, is the operating wavelength. By first differentiating the function describing the cumulative impact rate (per area), multiplying by D (, and re-integrating, we obtain the BRDF for the overall distribution.

Since both the micrometeoroid and debris cumulative impacts obey the form, cumulative number = D", the result is:

BRDF = n: x (n/(4-n)) x k ( x C N ~ , x Dm,~ ( /16 ~2 (9)

where n is the power index describing the cumulative number o f impacts versus particle size (in the neighborhood of the value of D , ~ , k is the ratio of crater diameter to particle diameter (D), CN is the predicted cumulative hit rate, and ~. is the wavelength.

The above equation involves the quantity D m u , which is the largest particle diameter to be used in the calculation. To determine the latter, we apply the following logic: if there is less than one (1) impact on the given optic, then there is no longer a meaningful definition of N, the areal impact density. Thus knowing the area of the optic, we compute the corresponding hits per meter. Referring to the predicted cumulative impact data versus particle size, we determine the value of D,,~.

As an example, consider an optic of area 100 c m 2. For one crater, we have an areal density o f 100 per m s (or 0.01 per cm ~ ), and thus this defines CND,.~. For debris, n = 2.5, and k = 7.0 (for the RAM surface). Reference to the particle plots of impacts on the RAM surface for the 1000 km, 60 degree orbit, gives the value D,.~ = 70 microns for debris. For mierometeoroids, n = 3.0, and k = 3.8, and D.,~ = 70 microns also.

Substituting into the equation for scatter (at 5 micron wavelength), we obtain:

For debris BRDF = 0.24 For meteoroids BRDF = 0.037

For the EARTH looking surface, we have n = 2.7, k = 3.25, and D,m = 25 microns, and only mierometeoroids apply. Thus we obtain (for 5 micron wavelength): BRDF = 2.2 x 10 -4

Thus, once more, the scatter for the RAM surface is much greater than for the EARTH surface. This effect is seen in Fig. 6, which shows computed scatter as a function of angle around the satellite (in the plane parallel to the Earth's surface) as well as the SPACE and EARTH-looking directions. Telescope

Impact damage and optical scatter 57

shroud shielding has not been included for these calculations, but will decrease all scatter values.

Although none of the above quotes for scatter can be considered precise, both approaches yield similar values (especially if the larger "level" quotes are used), suggesting the scatter for the RAM surface is enormous compared to that for the EARTH looking surface.

The data of Young gives BRDF as functions of off-specular angle. Inspection of these data reveal that the BRDF rapidly decreases over the range 0 to 10 degrees, and then follows a pseudo-exponential law for larger angles. To a reasonable approximation, the data for large angles (> 20 degrees) is given by:

BRDF = 5.4 x 10 ":s x (level) ~ x exp(-8.91 x 10 a x degrees) / L 2 (lO)

By integrating Young's data for BRDF versus off-specular angle, the total integrated scatter (TIS) can be obtained. A simple graphical integration gives:

TIS = 2.2 x 10 "s x BRDF( 0 degrees), or TIS = 5.5 x 10 .:7 x (level) s / X ~ (11)

with ~, in microns. Note that for BRDF ( 0 degrees) > 455, this implies scatter greater than the input, which is obviously nonsense. The conclusion is that for the larger degrees of scatter, the BRDF versus angle data must change its form, versus the lower cases (Young only presented data for contamination levels of 500 and below). Thus extrapolation of Young's data becomes suspect for large degrees of scatter. However, the estimates of scatter for the RAM surface, quoted above, are not within this uncertain region.

Brittle Material Response

All of the above pre-supposes that the optic behaves as if a metallic mirror with simple hemispherical craters. In reality, many mirrors (or lenses) are made of dielectrics and employ multiple thin layers (quarter-wave optical phasing logic). These materials are usually brittle. Upon hypervelocity impact, the damage consists of irregular craters with conchoidal surfaces, surrounded by star-cracks which can extend up to about 50 times the size of the impacting particle. To assess the optical scatter for these conditions it is necessary to invoke the the( .y of dielectric needles or cylinders as done by Van de Hulst (1957, 1981).

The evidence from LDEF indicates that impacts into brittle materials produce craters similar to those for ductile materials. However, the morphology is different, with the smooth-surface craters for ductile targets being replaced by a conchoidal, multi-crack surface for brittle targets, which is much rougher. Additionally, whereas ductile targets frequently display lips around the craters which stand proud of the initial surface, brittle targets frequently do not (presumably because the equivalent lip material was also brittle and cracked off). The other major difference is that brittle targets frequently display radial star cracking, with several (about 4 on average) cracks propagating away from the impact point over distances of up to 50 times the diameter of the impactor. Little systematic study has been done to date on these star cracks, though the work is ongoing by Jean-Claude Mandeville in France, a member of the LDEF Micrometeoroid and Debris Special Investigative Group (M&D SIG).

For the purpose of predicting cratering, the accepted meaning of a crater diameter is the value at the original target surface. However, the ductile target craters with lips can be about 50% larger if the diameter across the highest portion of the lips is measured, and up to 100% larger if the total diameter across the complete lip pattern is included. The previous methodology for computing fractional area damage did not account for these lips. If lips are included in the definition of areal damage, the values can clearly be up to 4 times as large, since area is proportional to the square of the size of the region considered. The inclusion of lips also has a large impact on the value of optical scatter owing to the k 4 term.

5g l). A[K,'~SON and A. W,~,[]s

Although there are several existing sealing laws describing simple cratering there are none, to our knowledge, describing the behavior of star cracks in brittle materials. Accordingly, we have formulated a possible equation describing them. This equation is:

rc/rp = (p'x/KI~) °4 (cJer)°4u °s rp °2 (12)

where r, is the radial extent of the crack from the impact point, rp is the impactor radius, p' is the effective density (defined below), Kxc is the target fracture toughness, c t and cp are the bulk sound speeds for target and projectile respectively, and u is the impact speed. Note that this equation predicts supralinearity, with the crack length increasing faster than the impactor diameter. This equation is derived by assuming that immediately following the outward compressive wave in the target the material develops hoop tensions. If these tensions are greater than the stress necessary to propagate an unstable crack at distance r from the impact site, then crack growth is assumed. The definition of effective density is based on the assumption of a Bernoulli fluid flow pressure state, and is given by:

p '= p,pe/((pr) °-~ + (pO°-5): (13)

where the p values are for impactor and target, respectively.

As examples of the consequential predictions, consider an impactor of aluminum (density of 2.8 g/cm 3) and a target of fused silica (density of 2.2 g/cm 3 ). Thus the effective density is 0.618 g/cm j. For fused silica the fracture toughness is 6.4 x 107dynes/cm 2 x cm °5. These values are reasonably typical of the conditions for impacts on LDEF for glass. Using the average LEO collision speed of 10 km/s, we predict:

for rp= 1.0 micron, r~/rp = 8.80, hence r c = 8.80 microns, for rp= 10.0 micron, ro/rp = 13.95, hence re = 139.50 microns, for rp= 100.0 micron, r~/rp = 22.11, hence re = 0.22 cm, for rp= 0.1 cm, r~/rp = 35.00, hence re = 3.50 cm, for rv= 1.0 cm, r Jr v = 55.53, hence re = 55.53 cm.

Note that for particle radii in the range I - 1000 microns, the cracks are predicted to extend in the range of 9 to 35 times the impactor size, in approximate agreement with observations. At present, there is no simple method of predicting the widths of these cracks. Assuming the crack widths to be, say, one- tenth the impactor diameter (dr), and taking an average crack to be 15 dp long, with 4 cracks per impact, the cracks represent an area of 6 dp 2, while the typical crater of about 5 dp wide has an area of about 20 dp 2. Thus, unless the cracks are much wider, or there are more cracks per impact, they will usually represent only a relatively small portion (e.g. 30%) of the total fractional area damage. However, for wider cracks, less-tough targets, higher impact speeds, or larger impactors, the fractional area due to the radial cracks could easily double that due to craters alone.

Optical Scatter for Brittle Materials

We have assessed the optical scattering for brittle, cracked targets. A typical package of interest is the multi-layered dielectric stack mirror. Frequently, such mirrors comprise a dielectric substrate (e.g. fused silica) with a thin (<2000 A) metallic reflecting coating, overlaid by a stack of alternating dielectric layers, each of one-quarter wavelength. The stack may have anywhere from only one dielectric layer up to several tens of layers. Depending on the operating wavelength, this results in optical coatings with thicknesses in the range of from about 0.3 micron (single layer, visible) up to perhaps 50 micron (multiple layers, infrared). Since impactors can produce craters with depths of about 3.5 times the impaotor diameter (e.g. for a RAM surface at 1000 km altitude and 60 degree inclination), even a 50 micron thick stack can be completely penetrated by a 14 micron particle, while the more typical 3 micron thick stack is penetrated by a particle of only 0.86 micron.

Impact damage and optical scatter 59

There is a fundamental difference between cratering in a ductile metal mirror and in a coated stack. For the metal mirror, the crater surface is still metallic, and thus still has high local reflectivity. However, penetration through the coating stack reveals the underlying substrate, and this usually has low reflectivity (e.g. 4% for silica). Thus, in essence cratering in coated optics is equivalent to punching holes in the mirror. While the holes will still give diffractive scattering (as with craters), the percentage loss of reflective area will also give a corresponding loss in overall reflectivity. Since these coating stacks are usually designed to maximize reflectivity (e.g. >98%), the loss due to the impactor cratering/'hole-punching" (with associated cracks) is significant.

An attempt to address the scattering caused by cracks can be done by treating them as equivalent to dielectric cylinders or needles, as done by van der Hulst (1981). Treating the cracks as cylinders with all dimensions large compared to the operating wavelength, the scatter is given by:

BRDF = (4a21/rtr2~.0) E2(ka0) per cylinder, (14)

where a is the radius of the cylinder, 1 is the length, r is the distance from the cylinder, ~. is the operational wavelength, 0 is the scatter angle (zero being the initial light direction), k is 2n/L, and E is the angular scatter function. If the crack pattern becomes "dense", such that cracks intercept with length 1, we have 1/12 cracks per unit area. Then we obtain:

BRDF ,=~ (4a2/~1~,0) E2(ka0) =# (8aZ/X 2) for 0 =# 0. (15)

Note that this implies the scatter depends only on the radius of the cylinders and the wavelength. The scatter from these cracks varies with the crack-width squared, whereas scatter from craters is proportional to the crater radius to the fourth power. Hence cracks are less efficient scatterers than are craters. Since it was shown above that the usual associated damage area of the cracks is also less than that of the craters, the result is that the craters are expected to dominate the overall scattering.

If the cracks are narrow compared to the operating wavelength, they behave as if dielectric "needles'. For this case the scatter is given by:

BRDF = (27tSa41)(mLl)2/(~. 3) per needle, (16)

where a is the radius of the needle, 1 is the length, and m is the "effective" refractive index. This "effective" index is based on the mismatch between the crack region and the surrounding medium. For scatter measurements done at wavelengths which are different from the "tuned" wavelength of the quarter-wave stack, the value of this index is similar to that for the individual layer materials. However, at the "tuned" wavelength, the effective index may be much higher, since the optical stack behaves as if a single dielectric with high refractive index (giving high reflectivity).

Since cracks are not truly circular in cross section, for both "cylinders" and "needles', the value of the "radius" is the equivalent one, given by one half of the square-root of the product of the crack width and the crack depth.

If the crack pattern becomes dense and intersecting, then the areal density of cracks (number per area) is given by N = 1/I z where 1 is the mean length between interceptions. Thus the equation for BRDF moves the "1" term from the numerator into the denominator.

As a check, consider the case of the dense crack pattern often observed due to hysterectic stress cracking after a sudden surface heating (e.g. by a pulsed laser, pulsed electron beam or a pulsed x-ray beam). Typically, the crack may have a depth equal to the optical stack which may be 3 microns, while the crack width may be about 300~ giving an equivalent crack radius of order 0.15 micron. For such intersecting dense crack patterns, the mean length of each crack may be about 20 microns. Assuming an interrogation wavelength of 0.5 micron (visible, not at the "tuned" wavelength), and an effective refractive index of 2.0, the predicted scatter is: BRDF = 1.12. This value is very large compared to the

6() D. AIKINSt)N and A. WAtts

initial virgin (undamaged) scatter value, which can be as low as BRDF = 10 .5 to 10 "7. Even for widely spaced cracks with lengths of 1000 micron (1 mm), the predicted scatter is BRDF = 2.24 x 10 "2. Such scatter values have indeed been measured for such damaged samples. Detailed Mie scattering calculations are required to accurately determine the scatter for a cracked dielectric multilayered stack. This would be especially true for scatter at the tuned wavelength of the stack. For this case the anticipated scatter is even higher, since the effective refractive index is larger (put another way, crack perturbations are worse for the high-reflectivity tuned case).

Note, that for needles the scatter increases with the needle width to the fourth power (similar to craters), and inversely with the wavelength cubed. For both cylinders and craters, scatter varies inversely with wavelength squared. Thus the precise level of scatter will depend strongly on the crack widths and the operational wavelength.

SUMMARY

We have performed first-order estimates of the probable modes of particle impact damage and consequential increases in optical scatter for satellite optics in LEO. The methodology requires use of the existing near-earth particle environment. Both simple ductile metal cratering and brittle material cracking have been addressed. The analyses include estimates of fractional area affected. For an orbit of 1000 km, inclination of 60 degrees and period of 6 years, even the RAM surface suffers from less than 1 percent areal damage due to simple ductile cratering. However, if star cracking in brittle materials occurs the affected areas rapidly increase. Note that the orbit chosen for analysis is one of the worst eases, involving a local peak in the man-made debris population.

The models used presently give reasonable agreement with the LDEF experimental data in terms of impact fluenees and directionality on the spacecraft body. However, the effects on optical surfaces is still under study. The analyses of increased optical scatter (BRDF) demonstrate strong dependencies on the details of crater sizes and crack lengths. For this reason there is a continuing need for better understanding of these impact responses.

Presently, our analyses indicate the potential for large increases in optical scatter for unshielded optics staring into the RAM, but only small increases for EARTH-looking eases.

We will perform future impact experiments on metallic and dielectric optics, and will directly measure the resulting optical scatter. These experiments will allow verification or modification of our estimates of damage modes and scatter.

REFERENCES

This work is done on behalf of the Air Force Phillips Laboratory, Kirtland AFB, NM, under contract F29601-91-C-0071, via a subcontract to SAIC, Albuquerque, NM.

Cour-Palais, B.G. et al. (1969). Micrometeoroid Environment Model - 1969 ( Near Earth to Lunar Surface), NASA SP-8013.

Kessler, D.J. and Reynolds, R.C. (1988). Orbital Debris Environment for Spacecraft Designed to Operate in Low Earth Orbit, NASA-TM-lO0471.

McDonnell, J.A.M. et al (1984). An Empirical Penetration Equation for Thin Metallic Films used in Capture Cell Techniques, Nature 309 237-240. Updates with Sullivan, K. (1991) private communication.

Young, R.P. (1976). Low-Scatter Mirror Degradation by Particle Contamination, Optical Engineering, Vol 15, No.6, Nov-Dec.

Van de Hulst, H.C. (1957, 1981). Light Scattering by Small Particles, Dover Publications.