Volevi la matematica, quindi eccola qui:
Devi conoscere il CoC della tua fotocamera, i sensori Canon APS-C di questo numero è 0,018, per Nikon APS-C 0,019, per i sensori full frame e la pellicola 35mm il numero è 0,029.
La formula è per completezza:
CoC (mm) = viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25
Un altro modo per farlo è la formula Zeiss :
c = d/1730
Dove d è la dimensione diagonale del sensore e c è il CoC massimo accettabile. Questo produce numeri leggermente diversi.
Devi prima calcolare la distanza iperfocale per l'obiettivo e la fotocamera (questa formula non è precisa con distanze vicine alla lunghezza focale, ad es. Macro estrema):
HyperFocal[mm] = (FocalLength * FocalLength) / (Aperture * CoC)
per esempio:
50mm lens @ f/1.4 on a full frame: 61576mm (201.7 feet)
50mm lens @ f/2.8 on a full frame: 30788mm (101 feet)
50mm lens @ f/1.4 on a Canon APS frame: 99206mm (325.4 feet)
50mm lens @ f/2.8 on a Canon APS frame: 49600mm (162.7 feet)
Successivamente è necessario calcolare il punto vicino che è la distanza più vicina che sarà messa a fuoco data la distanza tra la fotocamera e il soggetto:
NearPoint[mm] = (HyperFocal * distance) / (HyperFocal + (distance – focal))
per esempio:
50mm lens @ f/1.4 on a full frame with a subject at 1m distance: 0.984m (~16mm in front of target)
50mm lens @ f/1.4 on a full frame with a subject at 3m distance: 2.862m (~137mm in front of target)
50mm lens @ f/2.8 on a full frame with a subject at 1m distance: 0.970m (~30mm in front of target)
50mm lens @ f/2.8 on a full frame with a subject at 3m distance: 2.737m (~263mm in front of target)
50mm lens @ f/1.4 on a Canon APS frame with a subject at 1m distance: 0.990m (~10mm in front of target)
50mm lens @ f/1.4 on a Canon APS frame with a subject at 3m distance: 2.913m (~86mm in front of target)
50mm lens @ f/2.8 on a Canon APS frame with a subject at 1m distance: 0.981m (~19mm in front of target)
50mm lens @ f/2.8 on a Canon APS frame with a subject at 3m distance: 2.831m (~168mm in front of target)
Successivamente è necessario calcolare il punto lontano che è la distanza più lontana che sarà messa a fuoco data la distanza tra la fotocamera e il soggetto:
FarPoint[mm] = (HyperFocal * distance) / (HyperFocal – (distance – focal))
per esempio:
50mm lens @ f/1.4 on a full frame with a subject at 1m distance: 1.015m (~15mm behind of target)
50mm lens @ f/1.4 on a full frame with a subject at 3m distance: 3.150m (~150mm behind of target)
50mm lens @ f/2.8 on a full frame with a subject at 1m distance: 1.031m (~31mm behind of target)
50mm lens @ f/2.8 on a full frame with a subject at 3m distance: 3.317m (~317mm behind of target)
50mm lens @ f/1.4 on a Canon APS frame with a subject at 1m distance: 1.009m (~9mm behind of target)
50mm lens @ f/1.4 on a Canon APS frame with a subject at 3m distance: 3.091m (~91mm behind of target)
50mm lens @ f/2.8 on a Canon APS frame with a subject at 1m distance: 1.019m (~19mm behind of target)
50mm lens @ f/2.8 on a Canon APS frame with a subject at 3m distance: 3.189m (~189mm behind of target)
Ora puoi calcolare la distanza focale totale:
TotalDoF = FarPoint - NearPoint
per esempio:
50mm lens @ f/1.4 on a full frame with a subject at 1m distance: 31mm
50mm lens @ f/1.4 on a full frame with a subject at 3m distance: 228mm
50mm lens @ f/2.8 on a full frame with a subject at 1m distance: 61mm
50mm lens @ f/2.8 on a full frame with a subject at 3m distance: 580mm
50mm lens @ f/1.4 on a Canon APS frame with a subject at 1m distance: 19mm
50mm lens @ f/1.4 on a Canon APS frame with a subject at 3m distance: 178mm
50mm lens @ f/2.8 on a Canon APS frame with a subject at 1m distance: 38mm
50mm lens @ f/2.8 on a Canon APS frame with a subject at 3m distance: 358mm
Quindi la formula completa con CoC e HyperFocal precalcolata:
TotalDoF[mm] = ((HyperFocal * distance) / (HyperFocal – (distance – focal))) -(HyperFocal * distance) / (HyperFocal + (distance – focal))
O semplificato:
TotalDoF[mm] = (2 * HyperFocal * distance * (distance - focal)) / (( HyperFocal + distance - focal) * (HyperFocal + focal - distance))
Con CoC precalulato: ho tentato di semplificare le seguenti equazioni con le seguenti sostituzioni: a = distanza di visione (cm) b = risoluzione desiderata dell'immagine finale (lp / mm) per una distanza di visione di 25 cm c = ingrandimento d = FocalLength e = Apertura f = distanza X = CoC
TotalDoF = ((((d * d) / (e * X)) * f) / (((d * d) / (e * X)) – (f – d))) - ((((d * d) / (e * X)) * f) / (((d * d) / (e * X)) + (f – d)))
semplificata:
TotalDoF = (2*X*d^2*f*e(d-f))/((d^2 - X*d*e + X*f*e)*(d^2 + X*d*e - X*f*e))
Ancora più semplice con WolframAlpha:
TotalDoF = (2 * d^2 * e * (d - f) * f * X)/(d^4 - e^2 * (d - f)^2 * X^2)
O se nulla è precalcolato, ottieni questo mostro, il che è inutilizzabile:
TotalDoF = ((FocalLength * FocalLength) / (Aperture * (viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25)) * distance) / ((FocalLength * FocalLength) / (Aperture * (viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25)) – (distance – focal)) - ((FocalLength * FocalLength) / (Aperture * (viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25)) * distance) / ((FocalLength * FocalLength) / (Aperture * (viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25)) + (distance – focal))
semplificata:
(50*a*b*c*d^2*f*e*(d-f))/((25*b*c*d^2 - a*d*e + a*f*e)*(25*b*c*d^2 + a*d*e - a*f*e)
Quindi fondamentalmente usa CoC e HyperFocal ricalcolati :)