Lighting Standards Revisited: Introduction of a Mathematical Model for the Assessment of the Impact of Illuminance on Visual Acuity

Figures & data

Table 1 Lighting Benefit Metrics

Illuminance	Luminance	Function
Brightness-lx^Citation2	Brightness-nits^Citation2	Apparent brightness functions, VB2(λ) for low, outdoor applications and VB3(λ) for high, indoor applications^Citation2
Circadian-lx^Citation2	Circadian-nits^Citation2	Circadian illuminance function, VC(λ) for architectural lighting in homes, offices, schools^Citation2
Fovea-lx^Citation2 (Common illuminance values)	Fovea-nits^Citation2 (Common illuminance values)	Photopic luminous efficiency function, V(λ) for all uses as illuminance and luminance are derived from this function^Citation2
Periphery-lx^Citation2	Periphery-nits^Citation2	Scotopic luminous efficiency function, V’(λ), high and low mesopic efficiency functions, Vmh(λ) and Vml(λ), for lighting roadways, parking lots and parks^Citation2
IOL-lx	IOL-nits	Intraocular lens luminous efficiency function VIOL(λ)*

Note: *Proposed V_IOL(λ) as a new lighting benefit metric.

Abbreviation: IOL, intraocular lens.

Figure 1 Layout of experimental facility room (dimmable luminaires, illuminance meter, visual acuity chart, lighting control system, etc.).

Figure 2 Illumination distribution according to RELUX simulation tool.

Figure 3 Relative luminous efficiency functions. V(λ) is the original photopic luminous efficiency function. V_Panoptix(λ) is the modified photopic luminous efficiency function for pseudophakic eyes implanted with Panoptix IOLs. V_panoptix(λ) lower values = V(λ) for the lower transmittance values for the distant focal point of Panoptix IOL. V_panoptix(λ) upper values = V(λ) for the upper transmittance values for the distant focal point of Panoptix IOL.

Figure 4 Τhe spectral transmittance values for the distant focal point of Panoptix IOL in comparison with a 53-year-old crystalline lens. V_panoptix(λ) lower values = V(λ) for the lower transmittance values for the distant focal point of Panoptix IOL. V_panoptix(λ) upper values = V(λ) for the upper transmittance values for the distant focal point of Panoptix IOL.

Table 2 ICIR_Panoptix Values for Selected Lighting Sources

Light Source Technology	CCT (K)	ICIRPanoptix
		Upper Transmittance Values of Panoptix IOL	Lower Transmittance Values of Panoptix IOL
LED	2707	54.93%	54.05%
LED	3700	55.37%	54.38%
LED	4034	55.49%	54.46%
LED	6210	55.99%*	54.72%
FL	3146	55.27%	54.39%
FL	3751	55.50%	54.52%
FL	4784	55.73%	54.70%
FL	5671	55.96%	54.76%
Halogen - Incandescent	2556	54.89%	54.00%*
Halogen - Incandescent	2966	55.13%	54.19%

Note: *Maximum difference in transmittance values among the different light source technologies and CCTs.

Abbreviations: CCT, correlated color temperature; ICIR_Panoptix, intraocular-to-crystalline lens illuminance ratio for eyes implanted with a Panoptix intraocular lens; K, kelvins.

Figure 5 Actual relative spectral radiant flux emitted from the selected light sources.

Abbreviations: K, kelvins; LED, light emitting diode; FL, fluorescent, Halogen – Incandescent.

Table 3 Demographic and Clinical Characteristics of Study Participants

	N		Age (Years) (Mean ± SD) [95% CI] [Range]	Gender (Males/Females)	UDVA (Letters) (Mean ± SD) [95% CI]	Refractive Error (D) (Spherical Equivalent) (Mean ± SD) [95% CI]
	Participants	Eyes
SG	24	38	56.79 ± 7.41 [54.4, 59.1] [42–65]	6/18	52.68 ± 6.85 [50.5, 54.9]	− 0.25 ± 0.31 [−0.349, −0.151]
CG	28	50	52.28 ± 7.99 [50.1, 54.5] [40–65]	14/14	53.08 ± 10.00 [50.3, 55.9]	− 0.15 ± 0.52 [−0.294, −0.006]
p value	NA	NA	0.06	NA	0.88	0.72

Abbreviations: CG, control group (with crystalline lens); D, diopters; N, non-missing sample size; NA, not applicable; SD, standard deviation; SG, study group (with Panoptix intraocular lens).

Table 4 Differences in Uncorrected Distance Visual Acuity and Minimum Required Illuminance Level

	UDVA (Letters)				MRΙL (lx)
	Mean ± SD [95% CI]		Difference (550 lx – 20 lx)	p value	Mean ± SD [95% CI]
	20 lx	550 lx
SG	36.00 ± 8.31 [35.4, 40.6]	52.68 ± 6.85 [50.5, 54.9]	16.68	< 0.001*	191.05 ± 85.17 [164, 218]
CG	43.20 ± 13.29 [39.5, 46.9]	53.08 ± 10.00 [50.3, 55.9]	9.88	0.005*	122.00 ± 76.65 [101, 143]
Difference (CG - SG)	7.20	0.40	NA	NA	69.05
p value	0.04*	0.88	NA	NA	0.007*

Note: *p value < 0.05.

Abbreviations: CI, confidence interval; CG, control group (with crystalline lens); MRIL, minimum required illuminance level; NA, not applicable; SG, study group (with Panoptix intraocular lens); UDVA, uncorrected distance visual acuity.

Table 5 Experimental Measurements for Different Illuminance Levels

x (lx)	fCG	fSG	Difference in Percentile UDVA (%)	p value
	Mean ± SD [95% CI]
20	80.16 ± 18.94 [74.9, 85.4]	66.55 ± 8.83 [63.7, 69.4]	−13.61%	0.007*
40	86.36 ± 13.29 [82.7, 90]	77.93 ± 10.72 [74.5, 81.3]	−8.43%	0.03*
60	90.61 ± 10.59 [87.7, 93.5]	83.43 ± 8.58 [80.0, 86.8]	−7.17%	0.02*
90	93.89 ± 7.94 [91.7, 96.1]	87.39 ± 6.97 [85.2, 89.6]	−6.50%	0.008*
110	95.94 ± 6.56 [94.1, 97.8]	90.85 ± 6.86 [88.7, 93.0]	−5.09%	0.02*
130	97.18 ± 6.15 [95.5, 98.9]	92.38 ± 6.49 [90.3, 94.4]	−4.79%	0.02*
150	98.40 ± 3.00 [97.6, 99.2]	94.29 ± 6.32 [92.3, 96.3]	−4.11%	0.007*
170	98.46 ± 3.02 [97.6, 99.3]	95.66 ± 5.78 [93.8, 97.5]	−2.80%	0.04*
190	99.53 ± 1.78 [99.0, 100.0]	97.87 ± 3.81 [96.7, 99.1]	−1.66%	0.06
240	99.86 ± 0.69 [99.7, 100.0]	98.64 ± 3.14 [97.6, 99.6]	−1.22%	0.07
300	100.00 ± 0.00 [100.0, 100.0]	99.89 ± 0.47 [99.7, 100.0]	−0.11%	0.24
550	100.00 ± 0.00 [100.0, 100.0]	100.00 ± 0.00 [100.0, 100.0]	0.00%	NA

Note: *p value < 0.05.

Abbreviations: x, illuminance levels; f_CG, percentile UDVA of control group; f_SG, percentile UDVA of study group; CI, confidence interval; CG, control group (with crystalline lens); SG, study group (with Panoptix intraocular lens); SD, standard deviation; UDVA, uncorrected distance visual acuity.

Figure 6 Percentile UDVA for study and control group at different illuminance levels. . .

Abbreviations: CG, control group (with crystalline lens); SG, study group (with Panoptix intraocular lens); UDVA, uncorrected distance visual acuity; x, illuminance.

Table 6 Necessary Illuminance for Equal Percentile UDVA

x (lx)	xSGeq (lx)	Difference xSGeq - x (lx)	Relative Difference (xSGeq - x)/ x
20	35.27	15.27	76.34%
40	64.68	24.68	61.71%
60	89.60	29.60	49.33%
90	120.54	30.54	33.94%
110	137.86	27.86	25.33%
130	153.08	23.08	17.76%
150	166.57	16.57	11.05%
170	178.61	8.61	5.06%
190	190.41	0.41	0.22%

Abbreviations: x, illuminance levels of control group; x_SGeq, equivalent illuminance levels of study group; UDVA, uncorrected distance visual acuity.

Figure 7 Necessary additional illuminance of study group for equal percentile UDVA with control group (x_SGeq - x) for different illuminance levels. , where γ = (100–2.4) %.

Abbreviations: UDVA, uncorrected distance visual acuity; x, illuminance.

Figure 8 Additional percentile illuminance (x_SGeq - x)/x needed in study group for equal percentile UDVA with control group. , where γ = (100–2.4) %.

Abbreviations: UDVA, uncorrected distance visual acuity; x, illuminance.

Rea MS. The lumen seen in a new light: making distinctions between light, lighting and neuroscience. Light Res Technol. 2015;47:259–280. doi:10.1177/1477153514527599

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