ACTA 0 P H TH A L M 0 L O G I C A 71 (1993) 79-84

Evaluation of gray scale steps on Scheimpflug photographs

Wen Qian, Per G. Soderberg, Enping Chen, Karin Magnius and Bo Philipson

Eye Laboratory, S:t Eriks Eye Hospital and Department of Medical Biophysics, Karolinska Institute, Stockholm, Sweden

Abstract. A method for the calibration of gray scale den- sity in a Scheimpflug photograph was established. Based on the result of statistical analysis, it was found that va- riability in the film emulsion was insignificant if the measuring area 2 0.01 mm2. Each lens image should be calibrated with the reference gray scale in the same photograph. Photometric readings of the lens image was converted to gray scale levels. This conversion can be ob- tained from fitting photometric readings of the gray scale as a function of gray scale steps with a third order polyno- mial. Adopting t h i s calibration procedure, 95% of esti- mated nuclear densities are within f 3-5% of the real value.

Key words: Scheimpflug photography - photometry - gray scale standard.

In the present study a calibration method for Scheimpflug photography is presented.

Scheimpflug photography of the anterior seg ment of the eye is an important advance in objec- tive documentation of a lens opacity (Hockwin et al. 1982; Chylack et al. 1988). Scheimpflug photo- graphy is a useful method for clinical investigation on the development of an opacity in a lens as it is possible to compare the lens opacity at different time intervals.

There are many sources of variability in Scheimpflug photography, the principal ones are the quality of the film, the flash light intensity in the slit-lamp camera, and the film development

procedure (Hockwin et al. 1982). A variation in the photometer operation is also expected.

The photographic procedure has been stan- dardized to obtain a high reproducibility (Hock- win et al. 1982). However, in spite of the standardi- zation, variation in blackening of the gray scale standard among photographs taken at different occasions still exists (Chylack et al. 1988). This vari- ation can be minimized by calibration to the gray scale standard of each photograph (Chylack et al. 1988; Laser et al. 1990).

Chylack et al. (1988) suggested that the mean density for each gray scale step, which is estimated from a large number of Scheimpflug photographs, is used as an expected gray scale density. If the ac- tual gray scale density differs from the mean den- sity, a correction factor corresponding to the dif- ference between the expected and the actual is ap- plied to each gray step in the five-step scale. All in- termediate gray scale levels are calculated by li- near interpolation.

In another method (Laser et al. 1990), the gray scale is calibrated to the corneal peak scattering re- lated to an external source, to the gray scale steps related to an internal source and to a combination of those two.

The purpose of the present study was to estab- lish a calibration procedure for Scheimpflug photography based on only the internal gray scale step standard built-in the Scheimpflug camera.

79

Material and Methods

Instruments and film Slit-lamp photographs were obtained with a Top- con SL-45 slit-lamp camera according to the Scheimpflug principle. The Topcon SL-45 slit- lamp camera has a built-in five-step gray scale as an internal reference. The source for the slit light is simultaneously projected on the internal ref- erence. The light reflected from the reference scale is collected for imaging just beside the slit-lamp image of the eye media. In the present investiga- tion, one type of film (Kodak TX 5063) was used. Each film was developed according to a standard procedure (Hockwin et al. 1982).

To determine the variability of the photometer and the suitable size of the measuring area, ten rolls of film, each from a different patient, were evaluated. On each photograph, two different po- sitions in the image of gray scale step 2 were measured with a photometer incorporated in a Leitz microscope (Lindstrom & Philipson 1969). The magnification for the measurement was 125 times. The measuring spot was 0.03 X 0.03 mm. Each position was measured twice. The photome- tric readings were analyzed with an analysis of va- riance according to a hierarchial model (Snedecor & Cochran 1980a) (Appendix 1.1). The compo- nents of variance were estimated in accordance with Appendix 1.2.

The suitable size of measuring area was de- ducted from the present measuring spot (Appen- dix 1.3).

To determine the variability of reference gray

Sources of variance

scales among photographs, ten rolls of film, each from a different patient, were randomly selected. These films had been exposed during a time span of two years. Two photographs were randomly chosen in each roll of film. On each photograph, two positions at background and at each step, re- spectively, were measured photometrically. The photometric readings (FA) were analyzed statisti- cally with an analysis of variance for a mixed model (Bennett & Franklin 1963) (Appendix 2).

The significance ievel for all statistical analysis was set at p = 0.05.

sum of Mean Expected D.F. squares square mean

( ~ o - ~ P L A ) ~ ( 1 0 - 3 ~ ~ ) 2 square

Calibration The lowest significant order for a polynomial for photometric reading as a function of gray scale level was determined with an orthogonal compari- son (Freud & Minton 1979). Photometric read- ings were converted to gray scale levels by solving the polynomial with Newton-Raphsons method.

The accuracy of the present calibration proce- dure was tested by measuring step 2 and step 3 on the Scheimpflug photographs from ten randomly chosen patients. The photometric readings (FA) of step 2 and step 3 were converted to gray scale le- vels, respectively. A 95% tolerance limit (Beyer 1966) for estimations corresponding to step 2 and step 3, respectively, was calculated.

Results

The significance of the variability of the photometer and the variability among positions,

Table 1. Analysis of variance for photometric readings from gray scale step 2 on Scheimpflug photo-

graphs.

D.F. =Degree pf freedom. b = Number of positions = 2. n = Number of readings at the same position = 2.

80

Sources of variance D.F.

D.F. =Degree of freedom. Figure in bracket = F-value (p = 0.05). a =Number of films = 10. b = Number o f photographs within each film = 2. c =Number of gray scale steps = 6. n = Number of positions = 2.

Sum of Mean Expected squares square mean Test statistic

(10-*pA)4 (10-21A)2 square

respectively, was estimated (Table 1). The compo- nents of variance were obtained on the basis of the expression for the expected mean square (Table 1 . The component of variance for photometer, uE, and position, p2 , respectively, was 0.05 X and 3.48 X (ply, the component of variance for films, a*, was 17.75 X PA)^ (Appendix 1.2).

The result of the analysis of variance for ref- erence gray scale in Scheimpflug photographs is given in Table 2. It was found that the density of gray scale steps is different for different rolls of f5lm and for different photographs within the same film. The interaction factor forlllms and gray scale steps is also si@icant. However, the interaction

4

2

Table 3. Orthogonal comparison for determination of least significant polynomial order for density as a function of gray scale

step in Scheimpflug photographs.

Sum of Mean Sources of variance

Expected mean square

Test statistic

1 st-degree 1 148736 148736 a z + n o + bno + A , 4507.15 (4.06) BY AY

2nd-degree 1 9418 9418 o 2 + n o 2 + b n a + A y BY AY

285.39 (4.06)

3rd-degree 1 589 589 o + no + bna + A:, 17.85 (4.06) BY AY

4th-degree

5th-degree

17

8

17

8

o 2 + n a 2 + b n a + A , BY AY

o 2 + n o 2 + b n o + A 5 BY AY

0.52 (4.06)

0.24 (4.06)

Interaction (F-S) 45 1462 33 a + no + bna BY AY

A,,, = A term for the variance in the (m)th degree element. m = 1 ... 5. D.F. = Degree of freedom. Figure in bracket = F-value (p = 0.05).

6 Acta Ophthal. 71.1 81

factor for photographs and gray scale steps is insig- nificant.

The orthogonal comparison (Table 3) showed that a first, second and third degree element of the polynomial (photometric readings 0, versus gray scale levels (X)), are statistically significant, while a fourth and fifth degree element are insignificant. Therefore a third order polynomial

Y =a + b,X + b,X2 + b,X3 (Eq. 1)

is suitable for the calibration curve for each photo- graph. Here, a and b, ... b, are parameters specific for each Scheimpflug photograph.

A 95% tolerance limit for the calibrated value of step 2 and step 3 is 1.95 * 0.10 and 2.98 k 0.10, re- spectively.

Discussion

In the present study a method for calibration of Scheimpflug photographs was developed. It was assumed that the internal standard built in the camera is constant.

Scheimpflug photography is a suitable tech- nique for documenting nuclear cataract (Chylack et al. 1988). In the current study, preliminary meas- urements showed that the geometrical center in clinically not cataractous lenses had an average density of 1.69 gray scale levels. Therefore, the gray scale step 2 was selected to determine the suitable field size for measurement.

The result of the analysis of variance for the 0.03 X 0.03 mm spot showed that the variability of the photometer is negligible (Table 1). Therefore, one reading per spot is sufficient. The variability among positions is the main source of meas- urement variation (Table 1). This variation may be caused by local variability in the film emulsion. This source of variation can be reduced by increas- ing the size of the measuring spot. Increasing the size to 0.01 mmp, about ten times of the present measuring spot (b=10; Appendix 1.3), the va- riance due to variability in the film emulsion can

be reduced to its one tenth (-; Eq. A.2). The

precision for measurements with a spot size of 0.01 mm4 was estimated to be about 4% (Appendix 1.3). This precision is acceptable.

The result of the analysis of variance in Table 2

2

b aB

82

showed that the density of each gray scale step is not only different from film to film, but also from photo to photo within each film. The variation among films may be caused by variability of the quality of the film, the flash light intensity and the film development. The variation among photo- graphs may be caused by the variability of the flash intensity. Table 2 also showed that the increment of the photometric readings of five gray scale steps are different for different films (Interaction (F-S) in Table 2). This may also be due to variability in the film material and film development procedure. Thus, each photograph should be calibrated indi- vidually. By calibration of each lens image to its own gray scale standard, different photographs can be compared and the variation from the film material, the flash intensity and film development procedure could be avoided.

Photometric readings of five gray scale steps and one background yielded six data points for fitting a calibration curve. Six data points could determine a fifth order polynomial. However, the orthogonal comparison (Table 3) showed that almost all of the functional relation between film density and gray scale step number can be explained by a third order polynomial. Therefore, a third order polyno- mial was selected for the calibration procedure.

Regression theory implicates that the accuracy of a calibration curve obtained by regression in- creases with increasing number of steps on the ref- erence (Snedecor & Cochran 1980b). Therefore, the precision of the calibration could be further improved by increasing the number of steps on the gray scale reference for determination of the cali- bration curve.

The accuracy of the calibration curve was esti- mated by measuring the density of step 2 and 3 on the gray scale standard. Step 2 and 3 were chosen because their densities are comparable to that of the nuclear region of the lens. The 95% tolerance limits for the calibrated value of step 2 and step 3 were on the order of 3-5%. Thus, the calibration procedure includes a 5% risk that a density value expressed in gray scale steps is in reality 5% differ- ent from the value obtained. This implies that the precision of the established calibration curve is sa- tisfactory.

The above results showed that the present cali- bration method is accurate for the conversion of photometric readings to gray scale steps. Utilizing the individually established calibration polyno-

mid for each photograph, the variation of gray scale steps for different photographs is avoided. The present study provides a simple and s f i - ciently accurate method for the calculation of gray scale density of a lens image in a Scheimpflug photograph.

Appendix 1

1.1 Model for analysis of variance for photometric readings from gray scale step 2 on Scheimpflug photographs:

X.. = p + A i + B.. + E ~ ( ~ ) (Eq.A.1) ‘Jk J(1)

Here, p is the expected total mean, A, is a factor for the random variation among rolls of film (i = 1. ..a, a = lo), B is a factor for the random variation be- tween positions (i = 1 ... b, b = 2), E is a factor for the photometer variation (k = 1 ... n, n = 2).

1.2 The estimation of the components of variance for photometer, position and film.

The analysis of variance of Eq. A.l provides the mean square for the photometer, the position and the film, respectively. According to these mean squares, the components of variance for the photometer (a:), position (a;) and film (a:) can be calculated. The variance for the photometer, a:, equals the mean square for photometer. The variance for position, a;, is obtained taking the difference between the mean square for position and the mean square for photometer and dividing the difference by n. The variance for the film, a: , is obtained taking the difference between the mean square for film and the mean square for posi- tion and dividing the difference by b X n.

1.3 Analysis of suitable field size. Using a spot size of 0.03 X 0.03 mm, there is a va-

riability among positions, a: (Eq. A.l), due to the variability of the Glm emulsion.

If the suitable field includes b spots (each spot is 0.03 X 0.03 mm), the variability among fields (a:) equals the sum of the variability for the mean

j(I) k(ij)

2 2 -ando.. aB

(Eq. -4.2)

Here, a: corresponds to the variability among re-

6*

peated photometric readings on the same spot

The precision for measurement with the suit- (Eq. 1).

able field can be expressed as follows

af Precision = T X

(Eq. A.3)

Here, af is the variability among fields (Eq. A.2). X is the mean of photometric readings on the gray scale step 2.

Appendix 2

Model for analysis of variance for gray scale steps on Scheimpflug photographs:

In equation A.4, p is the expected total mean, A, is a factor for the random variation among rolls of film (i = 1 ... a, a = lo), Bj(i) is a factor for the random variation between photographs (i = l...b, b =2), yk is a factor for the fixed effect of steps (k= 1 ... c, c = 6), (AY) ,~ is an interaction factor for rolls of film and steps, (By@ is an interaction factor for photographs an steps, E ~ ( ~ ~ ) is a factor for the vari- ation among positions (I = 1 ... n, n = 2).

Acknowledgments

We are indebted to Professor Myron Wolbarsht for his comment on the manuscript and Mr. Lennart Wallerman for help with the experimental instruments. This study was supported by Wenner-Gren Foundation for Scien- tific Research, Karolinska Institutets forskningsfonder, Kronprinsessan Margeretas Arbetsnamd f6r Synska- dade, Swedish Society of Medicine, Gun och Bertil Stohnes Stiftelse, Synframjandets forskningsfonder, and Medical Research Council (project No. 4204).

References

Bennett C A & Franklin N L (1963): Ch. 7.63 Analysis in- volving both types of classifications. In: Statistical ana- lysis in chemistry and the chemical industry, pp 410- 417, John Wiley & Sons, Inc., New York.

Beyer W H (1966): Ch. 11.2 Tolerance factors for normal distributions. In: CRC Handbook of tables for prob- ability and statistics, pp 125-129, CRC, Cleveland.

83

Chylack L T Jr, McCarthy D & Khu P (1988): Use of Top- con SL-45 Scheimpflug slit photography to measure longitudinal growth of nuclear cataracts in vivo. Lens Res 5: 83-93.

Freund R J & Minton P D (1979): Ch. 6.3 Orthogonal polynomials; In: Regression Methods, pp 162-171. Marcel Dekker, Inc., New York and Basel.

Hockwin 0, Dragomirescu V & Laser H (1982): Meas- urements of lens transparency or its disturbances by densitometric image analysis of Scheimpflug photo- graphs. Graefes Arch Clin Exp Ophthalmol 219: 255- 262.

Hockwin 0, Lerman S & Ohrloff C (1984): Investigations on lens transparency and its disturbances by microdensitometric analyses of Scheimpflug photo- graphs. Curr Eye Res 3 15-22.

Laser H, Berndt W, Leyendecker M, Kojima M, Hockwin 0 & Cheyne A (1990): Comparison between Topcon SL-45 and SL-45B with different correction methods for factors influencing Scheimpflug examination. Ophthalmic Res 22 (Suppl 1): 9-17.

LindstrBm B & Philipson B (1969): Microdensitometer system for microradiopphy. Histochemie 17: 187- 193.

Snedecor G W & Cochran W G (1980a): Ch. 13 The ran- dom effects model. In: Statistical Methods, pp 238-254. 7th eds. The Iowa State University Press, Ames, Iowa.

Snedecor G W & Cochran W G (1980b): Ch. 17. Multiple linear regression. In: Statistical Methods, pp 334-364. 7th eds. The Iowa State University Press, Ames, Iowa.

Received on August loth, 1992.

Author’s address:

Wen Qian, Eye Laboratory, S:t Eriks Eye Hospital,

Sweden. S-112 82, Stockholm,

84