Photographic film

Introduction

It plays three essential roles in the treatment process of the information's optic. It can serve as:

  • A medium where the information is introduced in the optical system

  • A filter in the plane of frequencies to achieve the necessary extenuations

  • A medium to register the information at the exit of the system.

Process of registering and characterization

The structure of a black film is shown in the figure I-1.

An important quantity of halogen agent grains is in suspension in a gelatin support. The emulsion of a soft aspect is put between two supports to protect it. When the film is exposed to light, the grains that are absorbed by photons undergo a complex physio-chemical change (see figure I-2).

We are speaking of a registered latent image in the film while waiting for the development and the fixation.

The development is a chemical treatment that transforms the \(Ag\) halogen grain into metallic \(Ag\). The grains that have not been irradiated do not transform.

  • The fixation is a chemical treatment that eliminates the \(AgBr\) remaining while preserving the metallic \(Ag\). The \(Ag\) is strongly opaque in the optical frequencies. The opacity of the developed film depends therefore on the density of the silver grains in each region of the snapshot.

  • The exposure is defined by \(E(x,~y)= I_e (x,~y)\cdot T\). It is the incident energy by the unity of the surface : \(E\)  is in \(J/m^2\), \(I_e\) is in \(W/m^2\), \(T\) is the duration of the exposure in \(s\).

  • The transmittance is defined by :

τ ( x , y ) = I transmis ( x , y ) I incident ( x , y ) size 12{τ left (x,y right )= { {I rSub { size 8{ ital "transmis"} } left (x,y right )} over {I rSub { size 8{ ital "incident"} } left (x,y right )} } } {}

It is a local means, big before the size of the grain, but small before the fine structure of the details in the image.

  • The photographic density is defined by :

D = log 10 ( 1 / τ ) ⇔ τ = 10 − D size 12{D="log" rSub { size 8{ {} rSub { size 6{"10"} } } } left ( { {1} / {τ} } right ) dlrarrow τ="10" rSup { {} rSup { size 6{ - D} } } } {}

Hurter and Driffield (1890) show that \(D\) is directly proportional to the mass of \(Ag\) by the unity of the surface.

  • Curve H-D : it is the graph of \(D= f[log_{10}(E)]\)(see figure I-3)

When \(E<E_0 \Rightarrow D=D_v\) (density of the veil). The linear region is generally used where \(D= \gamma log_{10} (E) - D_0\).

The \(\gamma\) of the film depends on several parameters: the type of the film, the developing bath used, the time of development...

Figure I-5 shows the typical evolution of \(\gamma\) of a negative film in function of time of development.

The used film in incoherent optics

It transforms an intensity \(I_e (x,~y)\) received during the exposure into transmitted intensity after the development.

If the film is used in its linear part, then :

D = γ n log 10 ( E ) − D 0 = γ n log 10 ( I e . T ) − D 0 D= %gamma_n "log"_10 (E ) - D_0 = %gamma_n "log"_10 (I _e . T) - D_0

\(I_e\) can be linked to the transmitted intensity by the intermediary of the function of the transmittance defined by the preceding paragraph :

D = log 10 ( 1 τ n ) = γ n log 10 ( I e . T ) − D 0 D ="log"_10 left( alignl 1 over {%tau_n}right) =%gamma_n "log"_10 (I_e . T) - D_0
log 10 ( τ n ) = D 0 − γ n log 10 ( I e . T ) log_10 (τ _n) =D_0 - %gamma_n log_10 (I_e . T)
τ n = 10 D 0 . 10 log 10 [ ( I e . T ) − γ n ] τ _n = 10^{D_0} . 10^{log_10 {left [(I _e . T)^ {-%gamma _n}right]}}
τ n = 10 D 0 . ( I e . T ) − γ n = K n I e − γ n %tau_n = 10^{D_0} . (I_e . T)^{- %gamma_n}= K_n I_e^{- %gamma_n}
τ n = I tra I inc = K n . ( I e ) − γ n τ rSub n = { I rSub tra } over {I rSub inc } =K rSub{n} .(I rSub e) rSup { - γ rSub n }

\(\gamma_n\) and \(K_n\) being two positive constants, it is seen that the transmitted intensity by the film is not linear in function of \(I_e\). For example, if \(\gamma_n =1 \Rightarrow I_t\) .

To obtain a transmitted intensity that is proportional to the intensity of exposure, it is necessary to obtain a positive snapshot from the negative snapshot. For that, a second snapshot from the negative snapshot initially obtained is illuminated. If \(I_0\) is the incident intensity :

τ n = K n . ( I e ) − γ n = I t I 0 τ rSub n =K rSub n . (I rSub e) rSup {- γ rSub n} = {I rSub t} over {I rSub 0}
I t = I 0 τ n = I exposition du positif I rSub t = I rSub 0 τ rSub n =I rSub {exposition du positif }

The transmittance in intensity of the second positive snapshot will be therefore :

τ p = K ' n . ( I exposition du positif ) − γ ' n = K ' n . ( I 0 τ n ) − γ ' n τ rSub p = K' rSub n . (I rSub {exposition du positif} ) rSup { - γ' rSub n } =K' rSub {n} . (I rSub 0 τ rSub n ) rSup { - γ' rSub n}

By replacing the transmittance from the negative by its value in this last relationship :

τ p = K ' n . { I 0 [ K n . ( I e ) − γ n ] } − γ ' n τ rSub p =K' rSub n . left lbrace I rSub 0 left[K rSub n . (I rSub e ) rSup { { - γ rSub n } } right ] right rbrace rSup { - γ' rSub n }
τ p = K ' n ( I 0 ) − γ ' n . ( K n ) − γ ' n . ( I e ) γ n . γ ' n τ rSub p =K' rSub { size 8{n} } left (I rSub { size 8{0} } right ) rSup { size 8{ - γ' rSub { size 6{n} } } } . left (K rSub {n} right ) rSup { - γ' rSub { size 6{n} } } . left (I rSub {e} right ) rSup {γ rSub { size 6{n} } . γ' rSub { size 6{n} } }
τ p = Kp . I e γ p τ rSub p =Kp . {I_e} ^{γ_p}

\(K_p\) and \(\gamma_p\) are two positive constants. Here \(\gamma_p\) is the resulting gamma. We see that the transmitted intensity by the film is linear in function of \(I_e\). This is made possible by playing with the developing time. We can choose for example : \(\gamma_n = 1/2\) et \(\gamma_n =2\).

The used film in coherent optics

It transforms the incident intensity during the exposure in complex amplitude transmitted after development. It can also transform the complex incident amplitude during the exposure into a complex amplitude transmitted after development (by using the interferometric methods). In the two cases, the film is characterized by its complex transmittance:

t ( x , y ) = τ ( x , y ) e j φ ( x , y ) t (x,y )= sqrt {τ (x,y )} e rSup { j%varphi (x,y )}

where \(\varphi (x,~y)\) translates variations of phases that are introduced by the snapshot :

  • either by the unpredictable variations of the thickness of the gelatin

  • either by the variations of the thickness with the density of the Ag in the developed snapshot.

It is possible to eliminate the effects of these variation of thickness by using an immersion vat filled with oil at a convenient indication.

The transmittance of the vat and of the film can be written :

t n ( x , y ) = τ n ( x , y ) = K n . ( I e ) − γ n = k n | U e | − γ n t rSub n (x,y )= sqrt {τ rSub { size 8{n} } left (x,y right )} = sqrt {K rSub { size 8{n} } } . left ( sqrt {I rSub { size 8{e} } } right ) rSup { size 8{ - γ rSub { size 6{n} } } }= k rSub { size 8{n} } lline U rSub { size 8{e} } rline rSup { size 8{ - γ rSub { size 6{n} } } }

By realizing a positive:

t p ( x , y ) = τ p ( x , y ) = K p . ( I e ) γ p = k p | U e | γ p t rSub p (x,y )= sqrt {τ rSub { size 8{p} } left (x,y right )} = sqrt {K rSub { size 8{p} } } . left ( sqrt {I rSub { size 8{e} } } right ) rSup { size 8{ γ rSub { size 6{p} } } }= k rSub { size 8{p} } lline U rSub { size 8{e} } rline rSup { size 8{ γ rSub { size 6{p} } } }

It is desired in numerous cases that the film transform the amplitude into the square of its module, it suffices to take \(\gamma_p = 2= \gamma_n {\gamma_n}' = 2.1\)

The function of transfer of the modulation of the film

When the spatial period of variations of the luminous intensity becomes too small, it is possible that no other corresponding variation of density appears in the final snapshot. That is a sinusoidal variation of the incident intensity (see figure I-6) :

I ( x ) = I 0 + I 1 cos ( 2 π fx ) size 12{I left (x right )=I rSub { size 8{0} } +I rSub { size 8{1} } "cos" left (2π ital "fx" right )} {}

The rate of modulation of this intensity is defined by : \(M_i =\dfrac{I_1}{I_0}\)

We think back to the curve H-D of the film that is known for deducting the sinusoidal distribution of the effective intensity seen in the film (see figure I-7) :

I eff ( x ) = I 0 eff + I 1 eff cos ( 2 π fx ) size 12{I rSub { size 8{ ital "eff"} } left (x right )=I rSub { size 8{0 ital "eff"} } +I rSub { size 8{1 ital "eff"} } "cos" left (2π ital "fx" right )} {}

The registered rate of modulation is effectively deduced :

M eff ( f ) = I 1 eff I 0 eff size 12{M rSub { size 8{ ital "eff"} } left (f right )= { {I rSub { size 8{1 ital "eff"} } } over {I rSub { size 8{0 ital "eff"} } } } } {}

The function of transfer of modulation is defined by :

M ( f ) = M eff ( f ) M i ( f ) size 12{M left (f right )= { {M rSub { size 8{ ital "eff"} } left (f right )} over {M rSub { size 8{i} } left (f right )} } } {}

By varying \(f\) (the spatial frequency of the incident intensity) this operation can be repeated to determine the variation of the \(FTM\) of the film in function of the frequency. Typically we have an allure of a type passing low like the curve shows it in figure I-8.

The frequency of disconnection is variable (between \(50\) and \(2500 mm^{-1}\)for example for the photo plaque Kodak 649 F)

Whitening of photo snapshots

After the developing and the fixation of the film, a weak variation of thickness in the gelatin is established in the places where the \(Ag\) metallic remains. The process of whitening consists of removing the metallic \(Ag\) by a chemical treatment to keep this thickness variation in place.

Another whitening process is established to replace the metallic \(Ag\) of the gelatin by another salt of transparent \(Ag\) to the light, but presenting a bigger clue than the environmental gelatin.

The result is a structure of spatial variation of the constituent indication “a pure phase image.” Differences of the phase can be reached with this technique until \(2\pi\) and a resolution going to \(2500~mm^{-1}\).