Spotlight on the Corneal Back Surface Astigmatism: A Review

Figures & data

Table 1 Key Previous Estimates of Corneal Back Surface Astigmatism

Authors	Year	Instrument/Method	Values (D)
Dunne et al^Citation37	1992	Purkinje Images	0.23 (±0.02, n=40, F).
			0.37 (±0.03, n=40, M)
Oshika et al^Citation38	1998	Scanning Slit Video	0.18 (±0.16, n=50)
Liu et al^Citation39	1999	Orbscan	0.37 (±0.18, n=94) over 3.0mm
			0.52 (±0.25, n=94) over 5.0mm
			1.04 (±0.20, n=94) over 7.0mm
Dubbleman et al^Citation63	2006	Scheimpflug imaging	0.31 (n=114)
Kamiya et al^Citation64	2015	Pentacam HR	0.44 (±0.12, n=53)
Klijn et al^Citation22	2016	Pentacam HR	0.31 (±0.17,0.01 to 0.82, n=77)
Rydström et al^Citation40	2016	Pentacam HR	0.26 (±0.15, n=402)
Choi et al^Citation65	2018	Scheimpflug imaging	0.39 (±0.18, n=33)
Cui et al^Citation42	2019	Cassini	0.35 (0.04–0.89, n=117)
		Pentacam HR	0.29 (0.00–0.80, n=117)
Li et al^Citation43	2019	Sirius	0.31 (±0.17, 0.05–1.09, n=121)
Wylęgała et al^Citation48	2020	Galilei G6	0.44 (n=94) over 4.0mm
		Casia 2	0.52 (n=94) over 3.2mm
		Revo NX	0.05 (n=94) over 3.0mm

Notes: All mean values for astigmatism have been converted into plus cylinder format where necessary; Values in parentheses are ±sd and ranges according to the corresponding publication (reference number is in superscript); Details of instruments, or methods, used by each group of investigators are noted as cited in the relevant publication.

Abbreviations: D, units of astigmatic power (dioptres); F, females; M, males.

Figure 1 Diagram of a corneal section for the calculation of back surface radius. h₁= distance from the apex of the cornea and a peripheral location on corneal surface, t₁= thickness of the cornea at this peripheral location on corneal surface, t = thickness at the apex of the cornea, R₁ = corneal front surface radius, R₂ = corneal back surface radius.

Table 2 Partial Differential Equations for the Relative Error, , for in the Calculation of Corneal Back Surface Radius

	[2(t - B - √C)V - 2U]/V^2
	[4(K1t1) + 2t1 −2h1K1 + {2K2(t1+K1t1)/√[t1^2+(K1t1)^2]}]/V – U{2t1(1+K1)/ √[t1^2+(K1t1)^2]}/ V^2
	h1(2+2K5^2+4K5)+[2K8(K6+K7)]/V – U(K6 + 2K7)/V^2
	2{V[K11 - K12 + ([B-t+ √C]x[1- K9 –K10])] – U[1 - K9 -(h1^2t1^2/R1^3√C)]}/V^2

Notes: Where, with reference to Figure 1, h₁= distance from the apex of the cornea and a peripheral location on corneal surface, t₁= the length of the perpendicular stretching from this peripheral location on the corneal front surface to the peripheral corneal surface (ie, the thickness of the cornea at this peripheral location); t = thickness at the apex of the cornea; R₁ = corneal front surface radius, and A = h₁ - (h₁t₁/R₁); B= R₁ - √(R₁² – h₁²); C= t₁² + (h₁t₁/R₁)²; U= A² + (B + √C – t)²; V= 2(B + √C - t); K₁= h₁/R₁; K₂= B-t; K₃=K₁+1; K₄= h₁t₁; K₅= t₁/R₁; K₆= h₁/√(R₁² - h₁²); K₇ = h₁K₅²/√(t₁² + [h₁K₅]²); K₈ = B + √(t₁² + [h₁K₅]²; K₉ = R₁/√(R₁² - h₁²); K₁₀ = h₁²t₁²/R₁³√C]; K₁₁= h₁²t₁/R₁²; K₁₂= h₁²t₁²/R₁³.

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