Since its clinical introduction in 1927 by Brown,1 eye care professionals have been using the duochrome test (also known as bichromatic or dichromatic test)2 usually at the end of monocular/binocular refraction procedure3,4 to adjust the spherical component of the correction and to reach the subjective end-point of distance refraction. This test exploits the presence in the eye of longitudinal, or axial, chromatic aberration (LCA) (approximately 2 diopters between 400 and 700 nm)4 that provides different focal points for different wavelengths due to the relationship between the refractive index of the ocular media and wavelength. The duochrome test makes use of a typical distance visual chart split in two backgrounds, red and green (of approximately 620 nm and 535 nm respectively, according to the British Standard 36682), in which the same black stimuli are presented. Using these two different wavelengths, two different focal points are created that are expected to lie before and after the optimal focal point that, in the case of emmetropia, is expected on the retina. In an emmetropic eye, this optimal focal point placed on the retina is expected to correspond to a wavelength of approximately 570 nm (yellow light2,5). In the case of ametropia the optimal focal point is not on the retina, therefore, one of the two focal points, generated by the LCA, will be closer to the retina. This will increase the contrast of the stimuli on the background with the wavelength closer to the retina (red for myopia, green for hyperopia). The duochrome test is used during the refining of the spherical component of refraction and it is performed by asking the patient to indicate when letters appear equally clear on both backgrounds.

Considering the rationale of the duochrome test, changes in LCA across ages might affect its reliability. In the literature, LCA is typically measured in a broader range of wavelengths, usually from 450 nm to 650 nm, compared to those of the duochrome test. Moreover, literature on this topic shows conflicting results. For example, a study on fifty-eight subjects of different ages found a reduction in ocular LCA by a factor of four from 10 to 40 years to 70–80 years.6 The same authors also concluded that most of the reduction in LCA would occur at the onset of presbyopia.6 Another study,7 with only seven subjects, supported the LCA reduction with age. The reduction in LCA reported in this latter study, however, mainly concerned short wavelengths below 550 nm. On the contrary, longitudinal results reported by Ware8 regarding two subjects from 40 to 65 and from 30 to 55 years, respectively, showed essentially no change in ocular LCA in the 420–740 nm range of wavelengths. More recently, Tanaka et al.9 compared color visual acuity (VA) measured by Landolt rings with dominant-wavelengths equal to 607, 566, 488, and 440 nm on a white background in the age range 27–47 years. These authors concluded that a significant positive correlation occurs between LCA and age. However, this and other studies on this topic are cross-sectional studies and with investigation techniques that required subjects to assess clarity of a target to measure ocular LCA. This approach rests on the assumption that subject's ability to assess precision of focus does not vary with age or wavelengths.10,11 However, Howarth et al.12 speculated that smaller pupils and reduced transmission at the shortest wavelengths in older subjects can lead to illusory decline in ocular chromatic aberration and concluded that LCA is independent of age: LCA drop would be determined by ocular media scattering rather than refractive index changes.

The purpose of the present study is to compare the dioptric focal positions and the best visual acuities inferred from red, green, and white light defocus curves (DCs) with each other and with the results of the duochrome test and to investigate the applicability and relevance of the duochrome test in different age groups.

Table 2 shows the mean values of Φred and Φgreen calculated on the ELD and YG subjects (Φwhite is zero because the DCs of every subject were translated to set at zero the minimum of the DC taken with white background). As expected, mean data show positive dioptric values for red focal position (Φred) and negative dioptric values for green focal position (Φgreen) relative to white reference, with green-white mean dioptric distance (± standard deviation) of −0.12±0.17 (ELD) and −0.11±0.12 diopters (YG), and red-white mean dioptric distance of 0.08±0.13 (ELD) and 0.08±0.11 diopters (YG). As can be seen, the difference in absolute value with respect to white is slightly higher for green. Indeed, Φgreen reached statistically significant difference with respect to the zero-reference value for white (ELD p = 0.012; YG p = 0.039). This was not the case for Φred for both groups, although the threshold of significance was almost reached (ELD p = 0.064; YG p = 0.078). As expected, a clear difference (ELD p = 0.002; YG p = 0.008) was found between the red and green chromatic positions. In this respect, the mean LCARG (± standard deviation) was 0.20±0.16 and 0.18±0.18 diopters for ELD and YG group, respectively. No significant differences were found (ELD p = 0.622; YG p = 0.945) when comparing Φduo obtained with the duochrome test (ELD −0.02±0.19; YG 0.00±0.16 diopters) with the reference value Φwhite. The values of ΦmeanRG are −0.02±0.13 and −0.01±0.07 diopters for ELD and YG groups, respectively. Also in this case, no difference was found between ΦmeanRG and Φwhite (ELD p = 1.000; YG p = 0.641). Other p-values for the paired comparisons between Φred, Φgreen, Φwhite, Φduo, and ΦmeanRG are reported in Table 2 (left and right sides). Concerning the direct comparison between the two age groups, no differences in the dioptric powers were found between ELD and YG (p values are reported in the last column of Table 2 for each dioptric variable).

As far as BCVA is concerned (Table 3), the data show a peculiarity for the ELD group in the specific case of green. BCVA for ELD group was +0.03±0.14 and −0.02±0.11 logMAR for green and red, respectively, the two values being statistically different (p = 0.007). Not only compared to red, but also compared to white, for the ELD group BCVAgreen was found to be significantly worse (p = 0.007) than BCVAwhite (BCVAwhite = −0.06±0.12 logMAR). On the contrary, no difference was found between ELD BCVAred and BCVAwhite (p = 0.064). The scenario was different in the case of YG subjects. Indeed, the difference between BCVAgreen, BCVAred, and BCVAwhite was no more observed (−0.13±0.08, −0.13±0.11, and −0.15±0.08 logMAR for green, red, and white, respectively, with p>0.05 for all comparisons). The previous considerations concern the comparison between the three BCVAs in subjects belonging to the same age range. When comparing the two age groups, results from the YG group clearly showed lower logMAR values (better BCVA) compared to ELD using green background (BCVAgreenp = 0.004). Concerning white light (Table 3), the BCVA was still better in YG than ELD, but without reaching the statistical significance level (BCVAwhitep = 0.098). In general, the greatest BCVA difference between YG and ELD was found for green and the mean value of BCVAgreen in logMAR for ELD was the only one that was greater than zero (Table 3). Finally, when comparing DCs widths (Table 4), the mean value of the DC width in ELD for green (1.01±0.36 D) was higher than for red (0.77±0.21 D) and for white (0.84±0.35 D), but with no statistical significance. No significant differences were found between backgrounds and between age groups.

A first conclusion drawn from the present study is that the LCARG deduced from the DCs does not decrease with age (21–24 vs 55–66 years) in the spectral range between 535 and 610 nm. Indeed, the dioptric difference (LCARG) between the two colors used was found to be 0.20±0.16 diopters for the ELD group and 0.18±0.18 for the YG group. These LCARG results are consistent with some results reported in the literature.6–8,12,18 For example, Millodot6 reported that LCA depends on age, but the majority of the decrease was for wavelengths below about 540 nm, outside the spectral range of interest of the duochrome test.

Although equal extent of LCARG in the two age groups was found, differences cannot be excluded between ELD and YG concerning pupil size and higher order aberrations (HOAs) of the eye.18–20 However, these variables were not measured in this work. Conversely, experimental evidence of differences is here reported as a function of age in BCVA, especially in the case of green background. The observed worse BCVA in the elderly at shorter wavelengths (green compared to red) can be tentatively attributed to the increase of wavelength-dependent intraocular scattering.12 In turn, worse VA with green background compared to red could be the origin of the higher DC widths with green background (Table 4). In other words, a worse VA could make the eye more tolerant with respect to changes of the dioptric power from the optimal optical prescription. Even though it is not mentioned in the results section, the Spearman's rank correlation coefficient (rs) was computed to assess the relationship between BCVAgreen and Wgreen in the ELD group and, indeed, a significative good correlation was found (rs = 0.67, p = 0.017). In summary, despite the worse BCVA with green background compared to red in the ELD people and despite their general worse BCVA compared to YG subjects, a similar LCARG was found for the two age groups.

The results of the present study also show that the BCVA found with white background leaves subjects with a slight preferred focus towards the red that is independent from age. On the basis of the mean values of Φgreen and Φred shown in Table 2, it is possible to evaluate approximately which wavelength corresponds to Φwhite. For this purpose, through a simple model consisting of a single transparent medium and considering that the power of the eye is proportional to its refractive index, it is possible to assume that the relative dioptric power depends on wavelength as

The mean values of Φgreen and Φred shown in Table 2 associated with the wavelengths 535 and 610 nm respectively allow to deduce the parameters A and B and, in turn, the plot of Fig. 3 (line with diamonds). The dotted lines in Fig. 3 indicate the wavelength (576 nm) corresponding to Φwhite as deduced from Eq. (1). Since there are also models different from that of Cauchy21 to describe the dependence of the refractive index of transparent media on wavelength, another model mentioned by Thibos et al.22 was also adopted. The wavelength corresponding to Φwhite was substantially the same (line with empty circles).

Fig. 3.

Relative dioptric power (with respect to the abscissa of the DC minimum with white light assumed at Φwhite = 0) either obtained by Eq. (1) with A = −0.74634, B = 247,970, and the wavelength in nanometers, on the basis of the mean Φgreen and Φred shown in Table 2 associated with the wavelengths 535 and 610 nm (line with diamonds) or obtained by the model mentioned by Thibos et al.22 for the refractive index of the eye. The horizontal and vertical dotted lines indicate the wavelength (576 nm) corresponding to Φwhite = 0.

(0.06MB).

The slight preference towards the red with white background partially confirms some findings reported in previous studies. For example, Sivak and Bobier reported that the emmetropic eye is in a red focal position when unaccommodated.23,24 They concluded that an optical correction based on the equal clarity of letters on red and green backgrounds is expected to produce an overcorrection (excess minus) for myopic eyes and an undercorrection (insufficient plus) in case of hyperopia. In the present work, the trend in favor of focusing of the red component with white light was found to be present but slight, with the consequence that the average of the measured dioptric values with red and green (ΦmeanRG) was not statistically different from the power corresponding to the BCVA in white light (Φwhite). Thus, the slight preference for red at far distance does not compromise the possibility of using the duochrome test. This is also confirmed by the fact that Φduo is not statistically different from ΦmeanRG and Φwhite (Table 2).

Finally, it is worth noting that, the difference of about 0.20 D between red-green DC found in the present study for both groups, confirms the clinical appropriateness of the widespread use of 0.25 D step as the standard minimum difference in power between correcting lenses.

Experimental evidence at far distance is here reported of (i) a worse BCVA with green background in ELD subjects (55–66 years) compared to red background, (ii) a general worse BCVA of ELD compared to YG subjects, (iii) a slight focusing preference for red when using white light in both age groups. However, these differences do not compromise the possibility of using the duochrome test in clinical practice in the elderly. Indeed, a similar LCARG was found in ELD and YG groups and Φduo was not found to be statistically different from ΦmeanRG and Φwhite in both age groups.