The accuracy of the derivation of n- and k-values for an optical thin film coating material depends heavily on the accuracy of the spectrophotometric measurement data supporting the derivation. Any reflectance and/or transmittance errors will lead to errors in the resulting n- and k-values, which will in turn cause errors in the associated designs, and the actual coatings will have errors and depart from that which was intended. These derivations are an important part of the production of optical thin films, and need to be fully understood and carefully exercised. Possible causes of measurement errors , calibration procedures, and working standards are discussed. Tests for photometric accuracy are suggested. Techniques for calibrating spectrophotometers and obtaining accurate reflectance and transmittance data are reviewed.
Types of Reflecting Surfaces
It is advisable to clarify what is meant by several terms describing the types of reflectance and transmittance from a surface as illustrated in Fig. 1. A polished glass surface would have specular reflectance and regular transmittance (if it is not opaque). A ground glass surface would have diffuse reflectance and diffuse transmittance. Chalk would have diffuse reflectance. Varnished wood, polished stone, and glazed tile would have some specular component or gloss and some diffuse reflectance; it would have mixed specular and diffuse reflectance.
Figure 1. Three types of reflecting surfaces.
A special “ideal” case of diffuse reflectance is when the reflected light intensity follows the cosine or Lambert’s Law as seen in Fig. 2. An integrating sphere would ideally have a very highly reflecting and totally diffuse surface which is “Lambertian” in its reflectance.
Figure 2. Diffuse reflecting surfaces satisfying Lambert’s Cosine Law.
There are occasional papers in the journals and sections in texts on the fine points of the measurement of optical coatings such as Arndt et al.1, but seldom a review of “common” practice for a person new to the field. We will here attempt to help with that problem of “how to measure” before one embarks on using those measurements to determine n and k.
Different spectrophotometers have different f-number beams in their sample compartments and different minimum sample sizes in their beams. Older instruments may have been f/10 while some newer ones may be f/4. This beam convergence/divergence may need to be taken into account where coatings are angle sensitive. For example, a 100 GHz DWDM filter will shift a significant portion of its bandwidth (0.4 nm) with a one degree tilt. This means that such a filter cannot be properly measured with an ordinary spectrophotometer because the beam divergence will distort the band shape significantly. A typical beam in a grating instrument is also a millimeter or more wide and about a centimeter high at its smallest point. Again, the DWDM filter of ~1.5 mm square could not be measured properly in such a beam. A new family of instruments have appeared for the DWDM field such as Optical Spectrum Analyzers (OSAs). These are built around the tunable lasers, Gradient Index Lenses (GRINs), and the fiber optics of the field that they serve. They usually measure in Decibels (dB) rather than %T. Although an OSA is very different in detail, in the final result it is a spectrophotometer.
Infrared instruments are subject to effects of the absorption of water vapor and CO2 in the atmosphere. These are most noticeable at about 2.7, 3.2, and 6.2 Fm for H2O, and at 2.7, 4.3, and 15 Fm for CO2. If the atmosphere in the instrument changes from when the 100%T calibration was run to when the sample is run, there may be spectral artifacts at some of these wavelengths. If this is a problem, the instrument can be purged with dry nitrogen to eliminate the effects. Similar things can be said for regions of the ultraviolet (UV, 200-400 nm). The region from 40 to 200 nm in the UV is referred to as the vacuum ultraviolet (VUV) because the atmosphere absorbs at those short wavelengths and instruments must be evacuated to be effective. We understand that a dry nitrogen purge might be usable for some cases in the UV.
The typical spectrophotometer is designed to measure transmittance. We will later discuss ways to measure reflectance, but this section deals with transmittance only. The slit of the monochromator is typically imaged in the sample compartment; often near the center as shown, but sometimes at one side of the compartment. The reference beam is usually identical and toward the back of the compartment. The slit image is typically much higher than it is wide. We will assume that the light travels from left to right in the following figures.
A normal practice would be to run a 100%T calibration over the spectral range of interest with no sample in the beams and then a 0%T with an opaque sample in the sample beam while being careful not to interfere with the reference beam in the same sample compartment. The sample of interest is then placed in the sample beam and its transmittance spectrum scanned. Barring errors and instrumental non-linearity, the displayed result is the actual transmittance of the sample.
The 100% and 0% scans are not usually perfect as illustrated in Fig. 3. The corrected value for the sample %T at each wavelength would be 100*(C-B)/(A-B).
This assumes that the instrumental response is linear between curves A and B; but this might need to be tested using polished glass plates of known indices. In the case of dispersive instruments, the assumption may be more nearly valid than in FTIR instruments. Figure 4 shows the calibration of a typical dispersive spectrophotometer with a Schott4 N-BK7 plane-parallel piece of two-sides polished glass with “known” index versus wavelength. Such a piece might be purchased from Edmund Optics, etc. This shows the accuracy to be about 0.2%T over the spectral range at about 92%. The linearity of a UV-VIS-NIR spectrophotometer might be assessed by using “standards” of Fused Silica and Sapphire (which can also be obtained from Edmund Optics, etc.) as lower and higher indices materials than N-BK7.
Figure. 3. Plot of calibration for transmittance with 100% (A), 0% (B), and then the sample %T (C).
Figure 4. Linearity calibration of a typical dispersive instrument with Schott N-BK7 glass of known index values.
Potential Measurement Problems
There are a few problems to be aware of and to avoid. Figure 5c shows what can happen if a sample has some wedge in it. The beam is deflected and some of the transmitted light may be vignetted or not reach the detector. Different instruments have different sensitivities to wedge effects depending on the geometry of the optics between the sample and the detector. It is useful to rotate the sample about the horizontal beam axis to see if that influences the readings; this may be an indication of wedge in the sample. Similar problems can occur with thick samples like plates and prisms. As seen in Fig. 6e, a tilted thick plate can offset the beam and cause some of it to not reach the detector. Figure 6f shows how a thick plate or prism also would cause a focus shift which might be a problem for some instruments. Instruments have been seen which use a small integrating sphere at the detector to minimize these effects.
It may be possible to overcome some of these effects by reducing the beam diameter (f/number) on the left (input) side as it enters the compartment. This narrower beam may allow the transmitted beam to have some offset without causing vignetting or further loss of signal. The 100%T, of course, needs to be recalibrated with such a reducing aperture in place and some S/N is lost. If a sample is smaller than the normal sample beam at its smallest cross section, one can insert an aperture slightly smaller than the sample to be measured at the sample position and run a 100%T scan with no sample in place. The sample can then be added over the aperture and its transmittance spectrum run. This will reduce the S/N ratio in proportion to the area reduction of the sample beam; but this can be overcome by slower/longer data gathering.
Figure 5. The effect of wedge in a sample (c), measuring a 45° beamsplitter (d).
Coatings on beamsplitters that are on/in prisms need to be measured. A beamsplitter coated on a 45° prism can be measured by putting it together with an uncoated prism using uncured cement or an index matching fluid. One such fluid is “oil of wintergreen” (index ~1.536) which can be purchased at a pharmacy; another might be glycerin (index ~1.473). The transmittance of the assembly can then be measured as in Fig. 5d. The above-mentioned effects of offset and defocus need to be considered. Another problem is polarization. All spectrophotometers have some complex polarization effects in the beams. From earlier discussions, we know that coatings at anything but near normal incidence will have polarization effects. One practice is to measure the assembly such as that in Fig. 5d once and then rotate it 90° about the horizontal beam axis and measure it again. The average of the two scans should represent the effect of random polarization on the coating. The transmittance of beamsplitters at other than 45° in parallel sided prisms can also be measured this way.
Figure 6. Beam offset (e) and beam defocus (f) caused by a thick sample plate.
It is also possible to insert linear polarizers in both sample and reference beams (typically on the left where the beams enter the compartment) to only pass the desired polarization through the sample. There are also depolarizers which are crystalline in nature and change the state of polarization rapidly across the aperture of the beam so as to homogenize the polarization of the beams.
Since most spectrophotometers have been made for transmittance measurements, it is necessary to use attachments in the sample beam to accommodate the desired reflectance measurements. In some cases, the instrument manufacturers have attachments available; and in other cases there are a wide variety of attachments available from companies like Harrick2 and Labsphere3.
The simplest and first essential reflection attachment is illustrated in Fig. 7. The normally a horizontal transmittance beam is reflected upward by a mirror to the sample, and the beam is then reflected from the sample, and then is reflected again into the optical path by another mirror. The angle of incidence on the sample mirror should be as small as practical to avoid the changes in reflectance due to angle; 8° to 12° is typical and satisfactory. Error studies have shown this to be the best type of fixture for measuring antireflection and other low reflecting coatings.
The mirrors should actually be of a conic section shape to focus what would have been the slit image at the center of the sample compartment onto the reflectance sample and then back into the normal beam. Toroidal approximations of this are usually adequate.
Figure 7. A near-normal reflectance attachment.
There are several alternatives to calibrate this attachment. First, a 0%R line can be run with no sample in position. Then, a thin glass slide of known index such as N-BK7 can be placed in the sample position and the spectrum measured. If the glass is of index about 1.52 with no absorption in the region of interest, then the reflection should be about 8%. All subsequent samples can be compared with this calibration of the 8% reflectance. The glass slide can be verified by measuring its %T (which should be about 92%), if the absorption can be neglected.
Like the procedure above for %T, the corrected value for the sample %R at each wavelength would be D*(C-B)/(A-B), where the 100% is replaced by the known %R (D) of the reference glass as in Fig. 8.
Figure 8. Plot of calibration for reflectance with a known piece of glass (A), 0% (B), and then the sample %R (C).
Another alternative is to measure only the one-side reflectance of a known glass. This can be done several ways. As illustrated in Fig. 9, one approach is to coarse grind the back side of a sample so that the light reflected from the back is scattered widely, and hopefully very little of the light from the rear surface gets back into the beam that reaches the detector. The suitability of this approach will be more dependent on the f/number of the instrument. Some people further blacken the ground surface with a black making pen to reduce the reflection from the ground side. We recommend however to paint the back side of the flat witness with what amounts to an index matching fluid filled with carbon black (black paint). In this case, all the light reaching the rear surface enters the vehicle (which has an index near that of the glass, thus producing very little reflection at the interface) of the black lacquer (such as black KrylonTM spray paint) and is absorbed by the carbon black, thus only the front surface reflection is measured. It can be useful to use the last case illustrated in Fig. 9, where a single witness piece is painted black on one area for %R measurements and the rest is left clear for %T measurements.
Figure 9. Ways to treat %R witness samples for accurate measurement.
For calibration of one-side reflectance, there are a few additional geometries that can be used. Some facilities use a two-side polished witness glass of known index with a significant wedge between the bottom and top surfaces. The back surface should then be at such an angle that none of the light reflected from it gets back into the sample beam that reaches the detector. This wedge would then reflect about 4% depending on the exact index of the glass. A variant of this wedge technique is to have a coating sample on a thin plane parallel glass witness piece which is then oiled to such a wedge with index matching fluid such as oil of wintergreen or glycerin to create the same effect as the wedge alone.
A recommended example of eliminating the effects of the second side reflectance of a Reflectance Standard are shown in Fig. 10. Here a prism is used which has had all sides except the reference surface painted with black paint to capture the transmitted light through the first surface. This double light trap should be very effective as a replacement for the oiled wedge mentioned above. Prisms of N-BK7 and Fused Silica (without any coating) can be obtained from Edmund Optics, etc., for a reasonable price, and then painted with Black Krylon spray paint to be reflectance “standards.” However, simply painting the back of plane-parallel witnesses should be adequate for this work in most facilities.
Figure 10. A light trap possibility for a one-side calibration standard or and oil-on second-side reflection remover.
The accuracy of the derivation of n and k-values for a material depends heavily on the accuracy of the spectrophotometric measurements discussed above. Any %R and/or %T errors will lead to errors in the resulting n and k-values, which will in turn cause errors in designs, and the actual coatings will have errors and depart from that which was desired. This is an important part of the production of optical thin films, and it should be carefully understood.
1. D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. T. Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn: “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571-3596 (1984).
2. Harrick Scientific Corp., 88 Broadway, Ossining, NY 10562-0997.
3. Labsphere, Inc., Shaker St., North Sutton, NH 03260-0070.
4. Schott Glass Catalogs, http://www.us.schott.com