— Correlation of In-Vitro and In-Vivo SPF Testing Using the OPTOMETRICS SPF-290S — Some Practical Implications of Optical Reciprocity for Spectroscopic Instrumentation — Increasing Productivity Through the Automation of the SPF-290S — Summation in SPF Calculations

Application Note Number 1

Correlation of In-Vitro and In-Vivo SPF Testing Using the OPTOMETRICS SPF-290S

INTRODUCTION 
The Optometrics SPF-290S has been designed to measure the SPF values of various types of material containing sunscreen products. This application note describes the fundamental design of the instrument, the method used to make the measurements and tabulates the results of in-vitro and in-vivo measurements.

SPF-290S INSTRUMENTATION
The SPF-290S was designed specifically to measure the transmittance of material containing sunscreen products. Since these materials typically have low transmittance, the instrument was designed to detect very low levels of transmitted light.

The source is a high output continuous 125 watt xenon lamp. Light from the lamp passes directly through the sample. Since the output from the lamp has similar spectral characteristics to radiation from the sun, the illumination of the sample approximates in-vivo measurement illumination.

One problem associated with SPF measurements is the accurate spreading of the sample on the support medium (e.g., Transpore tape). The protocol requires a concentration of 2 µl/cm2 of sample spread evenly on the support medium. To achieve this, the SPF-290S is provided with a syringe capable of accurately dispensing 110 µl over an area of 55 cm2. To eliminate variations due to spreading technique, the instrument makes automatic measurements over the entire area, therefore integrating any irregularities due to spreading techniques.

Suncreens absorb and diffract light to varying degrees depending on the type and chemical composition of the sunscreen. Accurate measurements require that only absorbed light is measured by the detector and that as much apparent absorption due to diffracted light as possible is eliminated from the measurements.

To accomplish this, the sample is placed close to the entrance port of an integrating sphere. The integrating sphere and the close proximity of the sample to the entrance port combine to collect all of the transmitted light and most of the diffracted light.

In order to measure the transmittance of the sunscreen material over the UVA and UVB region of the spectrum, the light collected by the sphere must be diffracted by a high resolution monochromator with low stray light characteristics. The energy in each wavelength must be measured by a high performance detector. For an in-depth technical discussion on optical reciprocity, see Application note #2.

Because the samples have low transmittance, a monochromator and a highly sensitive photomultiplier tube are used to give the best monochromatic resolution and highest signal-to-noise ratio.

This SPF-290S monochromator and photomultiplier detection system was designed to provide the best results at low transmittance and therefore high SPF values. Alternate designs using diode array detectors are faster, but do not have the high signal-to-noise detection ratio required for the accurate and precise measurements of these types of samples.

SAMPLE AND METHODS
Twelve samples of varying types and SPF values were chosen in this study as representative of the types of samples frequently measured by cosmetic chemists. The samples were spread onto the support medium and measurements were made on the SPF- 290S over a 55 cm2 area. In each case, nine measurements were made and the instrument’s software calculated the mean SPF value and the standard deviation of each of the series of nine measurements.

RESULTS
The mean SPF values of the twelve samples are shown in the table below:

CONCLUSION
The data show that in-vitro measurements on the Optometrics SPF-290S give results that closely approximate in-vivo measurements for a wide variety of sunscreen materials.

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Application Note Number 2

Some Practical Implications of Optical Reciprocity for Spectroscopic Instrumentation

In optics, as well as many other disciplines, general principles can serve as powerful tools in both the design and performance analysis of various instrumental applications. Well known principles such as Conservation of Energy, Fermat's Principle, and Optical Reciprocity comprise a few such cases in point. This brief application note will address the last of these three, because its implications and utility can sometimes be misinterpreted.

Reciprocity relations in optics take various forms depending on the level of generality to be addressed. The Helmholz reciprocity theorem [Principles of Optics, sec. 8.3, Born and Wolf] is given in a format applicable to either wavefront or ray optics analysis. We will restrict the attention here to the latter case in order to emphasize the ray picture's utility for most spectroscopic instruments. [Fundamentals of Photonics, Saleh & Teich]. In that special case, if a ray of light traverses a linear optical medium, and is redirected through that medium back along the exit path, it will exactly retrace the incident path through that medium. [See Figure 1] Energy conservation ensures that the net efficiency is identical in either case. Though this statement is straightforward, its implementation must include the practical issue that light sources involve bundles of rays, so an effective path or efficiency analysis requires careful attention to an ensemble of rays, or properly chosen extrema. A series of examples illustrates this effectively.

In a ray optics picture, optical reciprocity implies that the path traversed in any medium, will be retraced exactly by a ray initiated along that same path, but in the reverse direction.

EXAMPLE 1. [Optical filter] This simple application addresses a beam of collimated light traversing a sample as in Figure 1, but with a collection of parallel rays, incident upon a medium. By reciprocity the return paths and the throughput efficiency would be precisely identical for either incident direction, and this remains so even in the presence of a non-uniform or absorbing index gradient. Note that each incident ray is identifiable with a corresponding ray in the reverse direction.

EXAMPLE II. [Diffraction grating] A significant portion of spectroscopic instrumentation requires these components [Diffraction Gratings, p.189, M.C. Hutley]. The input beam can be taken to be collimated and monochromatic, since generalized cases may be comprised of a (possibly continuous) collection of such rays. An incident beam directed along "zero order", will be dispersed into a number of discreet orders. Reciprocity is simply illustrated by considering one of the "n" diffracted orders. If that diffracted exit beam is re-directed back along itself, the path will be retraced with identical efficiency.

EXAMPLE III. [Reflective filter] Possible confusion is avoided in this case by noting that the exit beam from a reflective filter is by definition on the same side as the incident one, so reciprocity provides no connection between beams incident on opposite sides of such a filter, even if it is partially transmissive. That no such connection is expected is simply illustrated by a single sided mirror.

EXAMPLE IV. [Phase Conjugate Reflector] This reflective optic device that exhibits the extremely remarkable property that every incident ray is reflected exactly along its incident direction, independent of angle! Note that even a retro-reflecting corner cube fails to meet simple ray reciprocity due to the return ray displacement. Although phase conjugation provides an ideal realization of ray reciprocity, low efficiencies in passive forms, and high complexity for active ones, make it impractical for most spectroscopic work. Successful system applications have nevertheless been implemented in holography, advanced laser feedback design, and certain methods of wavefront restoration. [Optical Phase Conjugation, R.A. Fisher].

EXAMPLE V. [Integrating Sphere] We may now examine a case where light rays are present in all possible directions. Despite the apparent difficulty of tracking rays from a scattering surface, even here a simple model can provide many useful results. An integrating sphere with light originating inside and exiting through a small port is well approximated as a black-body source, the port itself acting as a "Lambertian" source that emits into the solid hemisphere, with radiance independent of angle. A loss-free scattering model retaining spectral reflection, is simulated by an inner surface covered by a mosaic of small randomly oriented mirror segments. Thus any ray, after multiple reflection, exits the port in a random (weighted) direction, or is re-absorbed at the source.

As a practical example, the efficiency of using such a sphere as a spectroscopic illumination source, may be compared with the reverse configuration where light is gathered for detection [See Figures 2 A&B]. Either configuration clearly retains the defining useful characteristic of such spheres, the ability to integrate a sample's response to light at all angles of incidence. To illustrate this we first consider an idealized extreme case, in which the spectrometer is restricted to generate or receive only perfectly collimated light. It is then clear from Figure 2-B (sphere in detection mode) that in the small port limit, nearly all of the light eventually lands on the detector. On the other hand the use of the sphere as the light permits almost no generated light to reach the detection system, since only a negligible portion of the random exiting angles are collimated. Reciprocity arguments apply only to the ray pairs, or wavefront portions, that re-trace their source-detector paths in both directions. Thus the asymmetry in this case must be analyzed in terms of the geometric losses.

To consider this in more detail we examine the case to follow, where all components are given physical dimensions, and proper cone angles replace perfectly collimated light. In a more realistic model, that retains very simple analysis, the source, detector element (resolution limited), spectrally and spatially mode matched spectrometer entrance and exit slits, and the sphere's port, are taken to have the same shape and area. Furthermore, the mono(poly)chromator accepts and emits F# 4 light cones, and the source is Lambertian. It is then straightforward to determine with the aid of Figures 2-A&B, that with correct imaging of the numerical apertures, the net efficiency in these two configurations is in essentially identical. In one case the primary loss is due to the fraction of light emitted from the integrating sphere into a cone of F# 4.

In the other, that same loss is incurred by the portion of the source filament's spherical emission that is imaged onto the spectrometer slit, again restricted by the cone angle of F# 4. (For light entering the sphere, the "exit" port loss is of course balanced by the emitting source's absorption factor in the two configurations.) Thus in a configuration simulating an actual implementation, we see that though the two configurations exhibit symmetry in net efficiency, it is not due entirely to reciprocity in this case.

CONCLUSION. A complete optical system could entail many more critical parameters and constraints besides efficiency and ray geometry. For example, the sample may have a threshold that limits the allowable light flux; in such a case the overall system performance may be largely determined by the detector's response characteristics. Various trade-offs may apply; in certain spectral regions photodiodes permit faster response and data

These two configurations illustrate an underlying symmetry with regards to losses (L) when source or detector are located within the sphere itself. The same fixed f # mono(poly)chromator, as well as mode-matched optics are assumed. If the light source and the sphere's exit port emit Lambertian patterns, the geometric system loss is the same in both cases i.e. the ratio of light in the solid cone angle defined by the f # to that of the Lambertian hemi-sphere. In either case it is incurred at the input lens to the spectrometer, in A for illumination and in B for detection.

Other assumptions entail modification. For a source modeled as a spherical emitter, an approximate factor of two loss is introduced in case A. Note that such loss does not necessarily apply to an alternate source location shown in B (outside sphere), since that light emitting geometry is not constrained by the f # of the spectrometer, so reflective nonimaging light concentrators can be utilized.

acquisition, whereas PMTs may exhibit a slower but much superior sensitivity, dynamic range, and signal/noise ratio, resulting in significantly greater measurement accuracy.

This brief study focused largely on only one particular principle, however both its utility and limitations were examined. The clear implication is, that to achieve a truly optimized system design, one needs to address all of the crucial performance parameters and constraints of that particular application, and in that process identify and implement relevant general principles.

[For related theoretical detail:JOSA-A, Dec 1986, p.2038, E. Wolf and M.Vesperinas]

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Application Note Number 3

Increasing Productivity Through the Automation of the SPF-290S

The automated X-Y Sampling Stage option for the SPF-290S will reduce the cost and improve both the repeatability and accuracy of SPF measurements.

This computer controlled accessory to the SPF-290S provides two modes of operation:

• Programmed Readings - multiple readings are taken across a sample, compensating for variations in sample spreading, and,
• Time-Based Mode - which measures changes in SPF values over time and can only be accomplished with the X-Y Sampling Stage option.

As a result of the X-Y stage's automation, technicians are freed to carryout other work while the SPF-290S takes the series of user-programmed measurements and computes the results.

Programmed Readings - Autoscan
In order to compensate for variations in sample thickness and to demonstrate sample spreading consistency, the X-Y Stage can read up to 12 pre-defined positions on the sample. The positions correspond to a set of non-overlapping reading circles that cover the sample area (Figure 1). These positions can be read using a choice of three modes: a fixed grid, a randomly generated grid or a user defined grid.

In the fixed grid mode, the operator can choose the number of scans for a sample run and the software will refer to its stored patterns for sample positions (see table below - Figure 2). The stored patterns are designed to provide a spread of measurements across the sample. The user can add scans to the pattern. The additional scan(s) are chosen from the "Subsequent Sequence" list (Figure 2). For example, you may have chosen 6 scans [at pre-programmed positions 4, 9, 12, 1, 7, 6] and then added an additional scan. The system will add position 10 from the "Subsequent Sequence" list for the seventh scan. This provides flexibility in the sampling process. A sample report for six scans is shown in figure 3.

The random grid mode is used when less than the full 12 positions are being read and the user wants to eliminate any bias in the choice of reading positions. The computer's random number generator determines which reading positions are to be used.

The user specified grid mode can be used when a smaller sample substrate (such as Vitroskin) is used.

Once set, the operation, data collection and reporting of results are performed automatically. The stage moves the sample on the holder into the light beam, takes the measurements, moves to the next position and continues until all the measurements have been completed.

Time-Based Mode
In the course of developing sun-screen formulations it may useful to evaluate them over a period of time to determine the effects of drying and exposure to air and light. The Time-Based Mode provides this function and produces reports of SPF value (Figure 4) and/or Cumulative Absorbance (Figure 5) as a function of time. Once a sampling position has been selected, the controller will make the initial scan, wait the specified time delay, and then repeat the measurements until the study is complete.

Twelve measurements can be taken with the time interval between measurements ranging from less than a minute up to an hour, giving a maximum test duration of eleven hours. During the time delay, the sample can be moved to an "out of beam" position to avoid exposure to the light beam. The sample can also be removed from the instrument for processing (simulated weathering for example), and then replaced for a measurement; a count-down timer on the screen alerts the operator to replace the sample for the next reading.

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Application Note Number 4

Summation in SPF Calculations

With the identification of a satisfactory substrate for in-vitro measurement of sunscreen protection factors (SPF), manufacturers of spectroradiometers dedicated to SPF measurements have used the equations described in A new substrate to measure sunscreen protection factors throughout the ultraviolet spectrum, B.L Diffey and J. Robson, J. Soc. Cosmet. Chem., 40, 127-133 (May/June 1989) as the basis for measurement calculations. Over the years, spectroradiometric software has provided other useful data to aid the photobiologist in their quest to develop new sunscreen products.

Recently, customers have expressed concern that companies have been cavalier in their use of simple summation to approximate integrals but use integral symbology in documentation and reporting.

The "integral" can be defined as designating simply a continuous sum. When this is based on an analytic equation then, in principle, an 'exact' computation is possible mathematically. However, when it is based upon a discreet set of points, such as data measurements, then it is by definition a sum, although it approaches an integral, and integral notation is often used to designate it. This sometimes causes confusion.

Somewhere in between is the case of tabulated data included in the expression, such as solar irradiance, etc. There is no analytic expression, but there may be values available at extremely small intervals. A choice is made as to how many points it makes sense to include in the computation, but again this is a sum. By using techniques such as trapezoidal approximations or triangular averaging at the end points, what is accomplished is that the sum is a slightly better approximation to an 'ideal integral'. However, it is understood that the ideal integral cannot actually be carried out, but better approximations to it can be achieved. How good those need to be requires that judicious choices be made, since truly continuous data is not available.

Optometrics Corporation has taken care to define its use of notation: summation (S) and integration (?) here signify a slightly different computation. When S appears in an equation the software implementation is exactly as described by the equation.

When we use an integral symbol we are using a software algorithm to better approximate the integral. However, for the reasons described above, sums are used in both methods and the notation distinguishes them.

For example, the equation we use for UVA/UVB ratio is:

To calculate the numerator we use the rectangular technique to approximate the integral as follows:

SPF equipment manufacturers are also being encouraged to be more accurate in their modeling,
mainly because users are becoming more sophisticated in their use of data gained from in-vitro
testing. Thus, Optometrics offers the choice of using the traditional equation for SPF as published
by Diffey or an integral approximation. Therefore, beginning with WinSPF V 2.1, the user
can select from two methods represented by the following equations:

implemented as follows:

In some cases, the differences in the results between the two methods is insignificant while in
others, the user may find the use of equation 5 to be clearly preferable to equation 3. Table 1
shows samples with wide-ranging protection factors and the affects of using the two methods of
calculating SPF.

Note that samples A through E are for lotion and cream sunscreen products with a typical spectral distribution of higher UVB absorption than UVA absorption, i.e. UVA/UVB from 0.25 – 0.50. Sample F is a fabric with a UVA/UVB ratio of 0.94. To be consistent, the erythemal UVA protection factor included in WinSPF reports is also available as a straight summation or rectangular approximation of the integral. Using WinSPF from Optometrics, the selection between the methods can be made in the Sample Setup form or the Change Calc. Method form by selecting either Rectangular Approximation or Rough Sum. To avoid arbitrary changes when reviewing sample data, Rough Sum is set as the default. If one wishes the older data to be recalculated using rectangular approximation, use Change Calc. Method and then save the data, overwriting the previous file.

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Application Note Number 5

Validation Kit for Optometrics SPF-290S

Formulators face two interrelated issues when testing In-Vitro SPF values in their labs, especially when they are new to the task: The level of confidence in the equipment and the learning curve associated with sample preparation. The Optometrics validation kit addresses both issues. It contains a calibration plate assembly and a set of standard formulations along with testing supplies.

The calibration plate includes non-volatile NIST traceable optical filters for testing photometric linearity and wavelength accuracy as well as one for In-Vivo correlation. Together with the ‘Comprehensive Test’ portion of WinSPF version 4.0, they provide a user-friendly tool for instrument validation.

The set of standard formulations allows the novice and experienced user alike to exercise their sample spreading skills and compare the results to known values of SPF 4 and SPF 15.

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