106 lines
4.0 KiB
Haskell
106 lines
4.0 KiB
Haskell
{-# LANGUAGE TemplateHaskell #-}
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{-# LANGUAGE NamedFieldPuns #-}
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{-|
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Basical optical types
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-}
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module Petzval.Optics
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(
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-- * IOR calculations
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Material(..), SellemeierMat(..)
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, BakedIOR(..)
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, ConstMat(..)
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-- * Optical elements
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, Element(..)
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, thickness
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, outsideRadius
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, material
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, roc
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, liftFp
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, specialize, bake
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) where
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import Control.Lens
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import Data.Maybe
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-- | An optical material, suitable to calculate indices of refraction
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class Material mat where
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iorAtWavelength :: Double -> mat -> Double
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-- | A material with a constant IOR of 1
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air :: mat
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-- | Calculates IOR based on the Sellemeier equation
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data SellemeierMat = SellemeierMat [(Double, Double)]
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deriving (Show)
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instance Material SellemeierMat where
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iorAtWavelength λ (SellemeierMat coeff) = sqrt $ 1 + (sum . map contrib $ coeff)
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where contrib (b,c) = b * w2 / (w2 - c)
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w2 = λ ^ 2
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air = SellemeierMat []
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-- | A material with a constant IOR
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newtype ConstMat = ConstMat Double
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deriving (Eq, Ord, Show)
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instance Material ConstMat where
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iorAtWavelength _ (ConstMat ior) = ior
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air = ConstMat 1
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-- | A representation of IOR as (previous,new) IOR at a surface
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data BakedIOR = BakedIOR Double Double
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deriving (Eq, Ord, Show)
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-- | An optical element
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data Element mat fp =
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-- | Refractive surface
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Surface { _thickness :: fp
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, _outsideRadius :: fp
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, _roc :: fp
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, _material :: mat
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}
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-- | Aperture stop
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| Stop {
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_thickness :: fp
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, _outsideRadius :: fp
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}
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deriving (Show)
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makeLenses ''Element
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{-
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-- | The space after the current element
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thickness :: Lens (Element mat a) (Element mat a) a a
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thickness inj (s@Surface{_thickness}) = (\nt -> s{_thickness=nt}) <$> inj _thickness
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thickness inj (s@Stop{_thickness}) = (\nt -> s{_thickness=nt}) <$> inj _thickness
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-- | The outside radius of the element. Rays that intersect the element beyond this radius are considered to have missed.
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outsideRadius :: Lens (Element mat a) (Element mat a) a a
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outsideRadius inj (s@Surface{_outsideRadius}) = (\nt -> s{_outsideRadius=nt}) <$> inj _outsideRadius
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outsideRadius inj (s@Stop{_outsideRadius}) = (\nt -> s{_outsideRadius=nt}) <$> inj _outsideRadius
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infinity :: (RealFloat a) => a
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infinity = encodeFloat (floatRadix 0 - 1) (snd $ floatRange 0)
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-- | The radius of curvature of an element. This is 1 for stops
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roc :: RealFloat a => Lens (Element mat a) (Element mat a) a a
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roc inj (s@Surface{_roc}) = (\nt -> s{_roc=nt}) <$> inj _roc
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roc inj (s@Stop{}) = (const s) <$> inj infinity
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-- | The material that a surface transitions into
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--
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-- For stops, this returns None and ignores being set.
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material :: (Material mat, Material mat') => Lens (Element mat a) (Element mat' a) (Maybe mat) (Maybe mat')
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material inj (s@Surface{_thickness, _outsideRadius, _roc, _material}) = (\nt -> Surface{_material=fromMaybe air nt, _thickness, _outsideRadius, _roc}) <$> inj (Just _material)
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material inj (s@Stop{_thickness, _outsideRadius}) = (const Stop{_thickness, _outsideRadius}) <$> inj Nothing
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-}
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-- | Translate a lens element from one FP type to another. E.g., can be used to convert from scalars to the types in an automatic differentiation tool.
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liftFp :: (Applicative f) => (fp -> f fp') -> Element m fp -> f (Element m fp')
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liftFp inj (s@Surface{_thickness, _outsideRadius, _roc, _material}) = (\t' or' roc' -> Surface{_thickness=t', _outsideRadius=or', _roc=roc', _material}) <$> inj _thickness <*> inj _outsideRadius <*> inj _roc
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liftFp inj (s@Stop{_thickness, _outsideRadius}) = (\t' or' -> Stop{_thickness=t', _outsideRadius=or'}) <$> inj _thickness <*> inj _outsideRadius
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{-# INLINE liftFp #-}
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specialize :: (Material mat) => Double -> [Element mat a] -> [Element Double a]
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specialize wavelength = (each.material) %~ (iorAtWavelength wavelength)
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bake :: (Material mat) => Double -> [Element mat a] -> [Element BakedIOR a]
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bake wavelength mat =
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snd $
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mapAccumLOf (each.material) (\n1 n2 -> (n2, BakedIOR n1 n2)) 1 $
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specialize wavelength mat
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