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zTe^2b>c?u9LzJx1f~uUE(jY2*=~4@g2v9qPs&v8T3&FxS?R$j-lx*r+Bg_JgMJsdf z8JrABpfVe>0SLHY>tZ8p#*T%62fkEQEeA(Z{6V&{r~Rk=)b9m@aM=nl)f4vU$N^@f wwzv^SR%A)+pDJ)bk>3D-CXf5wKiVA#Xdna+UfLGk_%2ow-XMTR+%FISI~PiK^8f$< diff --git a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.en.md b/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.en.md deleted file mode 100644 index 95d0fae2a..000000000 --- a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.en.md +++ /dev/null @@ -1,454 +0,0 @@ ---- -title: 'new course : overview' -media_order: 'objeto-fisico-imagen-virtual-haz-3-rayos-bb.jpg,objeto-fisico-imagen-virtual-pantalla-bb.jpg,objeto-imagen-posicion-tamano-bb.jpg,objeto-imagen-bb.jpg,objeto-imagen-3-rayos-bb.jpg,plano-imagen-real-convergencia-bb.jpg,plano-imagen-real-convergencia-pantalla-bb.jpg,plano-objeto-fisico-bb.jpg,vision-object-b.jpg,imagerie-rays-optics.gif,vision-object-image-2.jpg,vision-image.jpg,axe_opt.gif,plano-objeto-plan-image-bb.jpg,objeto-imagen-haz-3-rayos-bb.jpg,objeto-fisico-imagen-virtual-haz-3-rayons-pantalla-bb.jpg,plano-objeto-plano-imagen-real-pantalla-bb.jpg,sym_rev_2.gif,imagerie-rayons-lens-1.jpg,imagerie-rayons.jpg,imagerie-rays-optics.jpg' -published: true -visible: true ---- - - - -### What is optical imaging ? - -#### Objective - -* **Optical** $\Longrightarrow$ *visible* range + *near infrared* + *near UV* - -* to **realize optical images of physical objects** to be *seen with the naked eye* or to be *captured by an image sensor*. - -* **by the use of** *simple optical elements* which can be combined in *optical systems* to form *optical instruments*. - -#### Physical object - -* **Physical object** : *large* (compared to $\lambda_{optical}$) *volume* of matter (liquid or solid) whose *external surface can mentally be broken down in a huge number of microscopic surfaces*. - -* **Physical object point** = **point source** :
-\- *microscopic surface* part of the overall surface of the physical object.
-\- *emits* or *diffuses light in all direction* outside the volume. That means in equivalent ways : emits a *spherical wave* (_wave optics_), emits **light rays** (_ray optics_), emits *photons* (_quantum optics_) that **diverge from the object point**. - -* Point source **pencil of light** = **bundle of rays** : part of the *__light emitted by a point source__* that *intercept an optical system* or *pass through a limiting aperture*. - - -* **naked eyes** = **direct vision** of an object : *pencils* from all visible point sources of the object *intercept the pupil of the eye*. - -![](vision-object-b.jpg)
-Fig. 1. Direct vision : the pencils of each visible point souces intercept the pupil of the eye. - -#### Optical image - -* The object is seen from a **specific angle of view**, whose principal direction named **line of sight** defines (_when oriented positively in direction of the eye_) the **optical axis** of the imaging system. - -* The part of the *light that diverge from any point source* of the object and intercept the imager, after interaction *converges in a new point* in space named **real image point**, or *diverges from a new point* in space named **virtual image point**. - -* **Image** : *set of all real and virtual image points*. - -* **form consistency** between initial object and its image, but *shape distortions may appear*. - -![](vision-image.jpg)
-Fig. 2a. Image vision : an optical imager (rectangle) has modified the incident pencils. Only pencils from image points enter my eyes. here the image points are real. - -![](image-virtuelle.jpg)
-Fig. 2b. here the image points are virtual. - -#### Optical imager and basis physical principles. - -**Imager** : -* **Intercept part of the light** emitted or diffused by the physical object. - -* *modify the pencils* of light from each object point, to give a **new pencil** that :
-\- *converges* into a new point in space $\Longrightarrow$ *concentration of light energy* at this point. -\- *diverges* from on other new point in space $\Longrightarrow$ *no concentration of light energy* at this point. - -**Optical imager** : -* create a **true three dimensional** *image* of the extended object surface oriented towards the imager. -* use **refraction and/or reflection** phenomena. - -* An imager can be : individual **thin simple optical element** or **centered optical system** - -![](vision-object-image-2.jpg)
-Fig. 3a. Using refraction and/or reflection phenomena, an optical imager modifies all incident pencils from each point source,to give emerging pencils that actually focus the light energy of the source points into real image points, or pencils that diverge from virtual image points. Here a real image is observed. - - -![](Object-image_virtual.jpg)
-Fig. 3b. Here a virtual image is observed. - -#### Thin simple optical element - -* often has a **symetry of revolution about an axis**.
- -![](sym_rev_2.gif)
-Fig. 4. Simple optical element : refracting or reflecting element, rotationaly symmetrical around an axis. - -* **Thin** $\Longrightarrow$ *diameter $\gg$ thickness or depth*. - -* **Simple** : surfaces of *simple* optical element are *plane or spherical*. - -* **Thin optical elements** studied are :
-\- *plane or thin spherical refracting surfaces*.
-\- *plane or thin spherical mirrors*.
-\- *thin lenses*. - -#### Centered optical systems - -* **Combination** *of thin simple optical elements* **centered** *on a common axis* that becomes the optical axis of the system (_when positively oriented in direction of the incident light on the system)._ - -* *Interest* : can be **characterized as a whole**. - -![](axe_opt.gif)
-Fig. 5. Centered optical system : combination of thin simple optical elements, centered on a same optical axis. - -### What physical framework to describe optical imaging ? - -#### From mathematical idealization to physical reality - -* **Point** : mathematical concept of vanishing volume.
-has a *location* in space, but *no extension*, *no orientation*. - -* **Image point** physical meaning : the pencil emerging from the imager focuses on a so small volume that its *extension can be neglected*.
-\- extension of the volume can not be resolved with naked eye.
-\- surface illumated in the sensor plane is below the size of a pixel. - -* perfectly **stigmatic optical system** : *gives one image point for each object point* (**don't exist**). - -* **quasi stigmatic optical system** : *under certain conditions of use* a set of optical elements is *quasi-stigmatic* and so becomes an *imager*. - -* **Optical imager** = **quasi-stigmatic optical element or system** used to give images. - - - - -#### Framework of the paraxial approximation in Ray optics. - -* We use the concept of **light ray**, coming from *Ray optics* - -* **Ray optics** = **geometrical optics** - -* *When optical systems are considered stigmatic*, their study is carried out in the framework of **paraxial ray optics**. - -* **paraxial ray optics** = *paraxial approximation of Ray Optics* = *paraxial approximation of Geometrical Optics*. - -* A *light pencil that diverges from a point source*, is modified by an imager and after emergence, *converges to a real image point* or *diverges from a virtual image point*.

-  equivalent to

- \- *All rays emerging from a point source* are deviated by the imager and *cross back on a corresponding real image point*, or *their extensions intersect at a corresponding virtual image point*.

-$\Longrightarrow$ **knowledge of only two different rays** from a same point source through the imager **is sufficient** to determine image position. - -* For any object point of any imager, **trajectories of 3 specific rays will be specified**. - -![](imagerie-rays-optics.gif)
-Fig. 6a. Ray optics : 3 specific ray are specified (2 are sufficient) to locate the image point of any object point. In this figure the imager is a thin converging lens, and for this object position the corresponding image is real. - -![](imagerie-rays-optics-image-virtual.gif)
-Fig. 6b. In this figure the imager is a thin diverging lens, and for this object position the corresponding image is virtual. - -### How is modeled and characterized a thin simple optical element in paraxial rays optics? - -#### Thin simple optical element - -* **Thin simple optical element** = optical element whose *thickness can be neglected in front of diameter* **$\Longrightarrow$ represented by a plane (Elt)**. - -* Thin simple optical elements* are **rotationally symetrical around an axis** :
-$\Longrightarrow$ same optical behavior in all plane containing the axis of symetry.
-$\Longrightarrow$ *object point and conjugate image point belong to a same plane that contains the axis of symetry.
-$\Longrightarrow$ working in the **sectional view** corresponding to that plane is **sufficient**. - -* **Representation** on a sectional view containing the optical axis: *straight line [Elt] perpendicular to the optical axis*. - -* *Location* with its **vertex S** : intersection of [Elt] with the optical axis. - -#### Optical behavior - -* \- At each object point B corresponds to a unic image point B'.
-\- At each image point B 'corresponds a unic object point B :
-$\Longrightarrow$ **B and B' are conjugate points**. - -![](objeto-imagen-bb.jpg)
-Fig. 7a. The pencil coming from point source B intercepts the thin optical element. The corresponding emerging pencil converges on the point image B', which is a real image point because the light energy is concentrated at the point B'. -![](object-image-conjugate-virtual.jpg) -Fig. 7b. The pencil coming from point source B intercepts the thin optical element. The corresponding emerging pencil still diverges. But its extension shows that it diverges from an image point B' which is a virtual image point, because the light energy continues to disperse in space : no energy concentration in B'. - -* All object point (A ; B, C, ...) of an object plane (PO) perpendicular to the optical axis have conjugated points images (A' ; B', C', ...) in a same image plane (PI) perpendicular to the optical axis :
-$\Longrightarrow$ **(PO) and (PI) are conjugate planes**. -![](plano-objeto-plan-image-bb.jpg)
-Fig. 8. - -#### Coordinates to locate object and image points - -* Each point (object and image) is *projected perpendicularly on the optical axis* :
-\- point source B $\Longrightarrow$ point A on the optical axis.
-\- conjugate image point B' $\Longrightarrow$ point A' on the optical axis.
- -* *Distance of a point from thin imager* : **algebraic distance between imager vertex and point projection**.
- \- distance of point source B from imager [Elt] : **$\overline{SA}$**
-\- distance of conjugate image point B' from imager [Elt] : **$\overline{SA'}$** - -* *Distance of a point from optical axis* : **algebraic distance between point projection and point itself**.
- \- distance of point source B from axis [Elt] : **$\overline{AB}$**
-\- distance of conjugate image point B' from axis : **$\overline{A'B'}$** - -![](objeto-imagen-posicion-tamano-bb.jpg)
-Fig. 9a. - -![](object-image-plan-conjugate-virtual.jpg)
-Fig. 9b. - -#### Characterization of a thin simple optical element - -**4 points ** * located on the optical axis* that characterize optical behavoir : **S , C, F' and F** - -* **S** : **vertex** of the thin imager : *indicates its position* in space, and on the optical axis. -* **C** : **nodal point** : by definition *all rays* (or its extension) that *pass through nodal point C* has *unchanged direction* when leaving the thin optical element. Position characterizes by its algebraic distance from vertex S : $\overline{SC}$.
-The *nodel point* is a *center* (whose exact physical meaning depends of the type of thin simple optical element) - -* **F'** : **image focal point** = **second focal point** = **image focus** : *incident rays* (or their extensions) *parallel to the optical axis* (or their extensions), *after leaving* the thin imager, *pass through F'*. -* **F** : **object focal point** = **first focal point** = **object focus** : *incident rays* (or their extensions) *passing through F leave* (or their extensions) the imager *parallel to the optical axis*. - -which define **3 important planes, perpendicular to the optical axis** - -* **(Elt)** : representation of the **thin imager interface, contains S** : *incident rays* (or their extension) *change of direction when passing through (Elt)*. -* **(P')** : **image focal plane** = **second focal plane , contains F'** : *all incident rays parallel to each other* originated to a unic point at infinity *leave (Elt) to converge* (or their extension) *on a unic image point B' located in (P')*. Location of B' in (P') is the *intersection of the ray passing through C with (P')*. -* **(P)** : **object focal plane** = **first focal plane , contains F** : *all incident rays originated from a unic point source B leave (Elt) parallel to each other*, given an image point B' located at infinity, *in direction of the ray passing through C*. - -and **2 important algebraic distances** - -* **$f'=\overline{SF'}$** : *algebraic distance from thin imager (Elt) to image focal plane (P)* :
- -* **$f=\overline{SF}$** : *algebraic distance from thin imager (Elt) to object focal plane (P)*. - - -### Important significations of focal planes - -#### Image focal plane : - -* *Physical sense* :
**object B at infinity $\Longleftrightarrow |\overline{SB}| \ll |f|$**. - -* **Object at infinity (P) $\Longleftrightarrow$ object in (P')**, can be **viewed by naked eye** whether *convergent or divergent* optical element. - -![](plano-imagen-real-convergencia-bb.jpg)
-Fig. 10. Example : direct vision of the universe through a telescope (telescope is not a thin imager, but same image focal plane defintion). - -* **Object at infinity (P) $\Longleftrightarrow$ object in (P')**, to be **captured by an image sensor** *if convergent optical element*. -* -![](plano-imagen-real-convergencia-pantalla-bb.jpg)
-Fig. 11. Example : picture taken with a telephoto lens (telephoto lens is not a thin imager, but same image focal plane defintion). - -#### Object focal plane (P) - -* *Physical sense* :
**image B' at infinity $\Longleftrightarrow |\overline{SB'}| \ll |f'|$**. - -* **Object in (P) $\Longleftrightarrow$ image at infinity** - -![](plano-objeto-fisico-bb.jpg)
-Fig. 12. Examples : the object can be the bulb of a lighthouse, or the film in a non-digital cinema projector (with quasi-parallel emerging beams in both cases, to illuminate front and far). - -### How to determine the image given by a thin simple optical element ? - -#### Graphical study - -##### Two different scales - -* Object and image : *tranverse sizes $|\overline{AB}|$, $|\overline{A'B'}\;\;\ll$ distances from optical element* along optical axis $|\overline{SA}|$ , $|\overline{SA'}|$.
-$\Longrightarrow$ dimensions perpendicular to optical axis $\ll$ dimensions along optical axis - -* So **Accurate graphical study** $\Longrightarrow$ *greatly magnify scale perpendicular to optical axis*. - -![](objeto-imagen-posicion-tamano-bb.jpg)
-Fig. 13. - -##### Determining of conjugate points - -From given point (object or image) **3 specific light rays can be drawn** ( only 2 required), whose *intersection gives the conjugate point* : - -![](objeto-imagen-3-rayos-bb.jpg)
-Fig. 14. - -* **[Ray1]** : Incident rays (or their extensions) passing through the object focal point F leave (or their extensions) the imager parallel to the optical axis. -* **[Ray2]** : Incident rays (or their extensions) parallel to the optical axis pass (or their extensions), after leaving the thin imager, through the image focal point F'. -* **[Ray3]** : Incident ray (or its extension) passing through point C has unchanged direction when leaving the thin imager. - -##### Consequences from focal points definitions - -* **Incident rays parallel to each other** intersect on a *same point in the image focal plane* (P').
-(location : intersection of (P') with [Ray3]) - -* **Emergent rays parallel to each other** diverge from a *same point source located in the object focal plane* (P).
-(location : intersection of (P) with [Ray3]) - - -##### Determining the emergent ray corresponding to any incident ray - -* **deflection of a ray by a thin optical element** : *local interaction the point of impact* (refraction or reflection) between incident ray and thin optical element $\Longrightarrow$ *independent of the distance of the point source*. - -* so consider **point source B to infinity** $\Longrightarrow$ image point *B' would be in the image focal plane (P')*. - -* **ray from B** (to infinity) **passing through point C** has *unchanged direction* $\Longrightarrow$ *location of B' in (P')*. - -* **Emerging ray** (or its extension) = *straight line between impact point and B'*. - -![](rayon-incident-quelconque-5.gif)
-Fig. 15. - - -##### Determining the incident ray corresponding to any emergent ray - -* **deflection of a ray by a thin optical element** : *local interaction the point of impact* (refraction or reflection) between emergent ray and thin optical element $\Longrightarrow$ *independent of the distance of the image point*. - -* so consider **image point B' to infinity** $\Longrightarrow$ point source *B would be in the object focal plane (P)*. - -* **emerging ray towards B** (to infinity) **passing through point C** has *unchanged direction* $\Longrightarrow$ *location of B in (P)*. - -* **incident ray** (or its extension) = *straight line between impact point and B*. - - -#### Analytical determining of conjugate points - -##### Distance of the conjugate point from thin optical element - -* deduced from the **thin optical element equation** - -* **thin optical element equation** = **thin optical element formula** - -* will be given for :
-\- *thin spherical mirror equation*
-\- *thin spherical refracting surface equation*
-\- *thin lens equation*
-(will be demonstrated in level foothills) - -##### Distance of the conjugate point from optical axis - -* deduced from the **transverse magnification $M_T$**. - -* **transverse magnification** = **lateral magnification** - -* **Definition** : **$M_T=\dfrac{\overline{A'B'}}{\overline{A'B'}}$** - -* **$M_T>0$** *$\Longleftrightarrow$* **erect image**
- **$M_T<0$** *$\Longleftrightarrow$* **inverted image** - -* **Expression** : *depends on* type of *simple optical element* :
- will be given for :
-\- *thin spherical mirror equation*
-\- *thin spherical refracting surface equation*
-\- *thin lens equation* - -* **algebraic value of $M_T$** : is a *function of $\overline{AB}$ and $\overline{A'B'}$*
-$\Longrightarrow$ depends on conjugate points locations
-$\Longrightarrow$ **does not characterized the optical element** itself. - -### How to characterize the action of an imager ? - -#### Characterization of an extended object - -* Extended object [AB] or [B$_1$B$_2$], **perpendicularly to the optical axis** :

-\- characterized by the *algebraic transverse size* (distance between its extremities) : **$\overline{AB}$** or **$\overline{B_1B_2}$**

-\- or characterized by the *apparent angle* (in algebraic value or not) *substended by the object at nodal point* of the eye (direct vision) or nodal point of the thin imager : **$\alpha$** or **$\overline{\alpha}$** - -* Extended object [A$_1$A$_2$] **along the optical axis** :

- characterized by the *algebraic longitudinal size* (distance between its extremities) : **$\overline{A_1A_2}$** - -#### Characterization of its conjugate extended image - -* Extended image [A'B'] or [B'$_1$B'$_2$], **perpendicularly to the optical axis** :

-\- characterized by its *algebraic size* (distance between its extremities) : **$\overline{A'B'}$** or **$\overline{B_1'B_2'}$**

-\- or characterized by the *apparent angle* (in algebraic value or not) *substended by the object at nodal point* of the eye (direct vision) or nodal point of the thin imager : **$\alpha$** or **$\overline{\alpha}$** - -* Extended image [A'$_1$A'$_2$] **along the optical axis** :

-characterized by the *algebraic size* (distance between its extremities) : **$\overline{A'_1A'_2}$** - -#### Characterization of the imager action on an extended object - -The imager gives an image of an object. The **characterization of imager action** depends on *how the object and the image are characterized*. - -##### Transverse magnification of the extended object - -* *Object and image* both **characterized by their algebraic transverse sizes** :
-**$\Longrightarrow$** *imager action* characterized by the **transverse magnification $M_T$**

-**$M_T=\dfrac{image\:size}{object\:size}=\dfrac{\overline{A'B'}}{\overline{AB}}$** - -##### Apparent magnification of the extended object - -* *Object and image* both **characterized their apparent angles** :
-**$\Longrightarrow$** *imager action* characterized by the **apparent magnification $M_A$**

- -**apparent magnification** = **angular magnification** - -**$M_A=\dfrac{image\:apparent\:angle}{object\:apparent\:angle}=\dfrac{\overline{ \alpha '}}{\overline{ \alpha }}$**

-or $M_A=\pm\dfrac{ \alpha '}{ \alpha }$, with sign + when erect image, sign - when inverted image.

- -![](apparent-magnitude-magnifying-glass-1018.gif)
-Fig. 16. In this experiment, the observed object is located at a certain distance from the magnifying glass, as well as the eye of the observer. For these conditions of use, the magnifying glass gives a magnification of +2.5. There are optimum conditions for using the magnifying glass (see chapter "optical instruments"). - -!!!! *BE CAREFUL*
-!!!!An apparent angle depends on distance from the object or the image to the nodal point of the observing system (human eye or telephoto lens of a camera for example) $\Longrightarrow$ more accurate definitions of apparent angles will be necessary (see chapter "optical instruments"). - -##### Longitudinal magnification of the extended object - -* *Object and image* both **characterized by their algebraic longitudinal sizes** :
-**$\Longrightarrow$** *imager action* characterized by the **longitudinal magnification $M_L$**

-**$M_L=\dfrac{image\:size}{object\:size}=\dfrac{\overline{A'_1A_2'}}{\overline{A_1A_2}}$** - - - - - - - - - - - - - - - - - - - - diff --git a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.es.md b/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.es.md deleted file mode 100644 index b3829d433..000000000 --- a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.es.md +++ /dev/null @@ -1,7 +0,0 @@ ---- -title: 'nuevo curso : síntesis' -published: true -visible: true ---- - -nuevo curso : síntesis \ No newline at end of file diff --git a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.fr.md b/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.fr.md deleted file mode 100644 index b576efe4d..000000000 --- a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/03.optical-systems-vergence/02.optical-systems-vergence-overview/cheatsheet.fr.md +++ /dev/null @@ -1,413 +0,0 @@ ---- -title: 'nouveau cours : synthèse' -published: true -routable: true -visible: true -lessons: - - slug: gravitation-electrostat-magnetostat - order: 2 ---- - -### Qu'est ce que l'imagerie optique? - -#### Objectif - -* **Optique** $\Longrightarrow$ domaines *visible* + *proche infrarouge* + *proche UV* - -* **Réaliser des images optiques d'objects physiques** pour être *vues à l'oeil nu* *ou* pour être *capturées par un capteur d'image*. - -* **par l'utilisation** d'*éléments optiques simples* qui peuvent être combinés en *systèmes optiques* pour former des *instruments optiques*. - -#### Object physique - -* **Objet physique** : *volume* de matière (solide ou liquide) *grand* (comparé à $\lambda_{optical}$) dont *la surface externe peut être décomposée mentalement en un très grand nombre de surfaces microscopiques*. - -* **Point objet physique** = **source ponctuelle** :
-\- *surface microscopique* partie de la surface totale de l'objet physique.
-\- *émet* or *diffuse la lumière dans toutes les direction* en dehors du volume. Se dit de façons équivalentes : émet une *onde sphérique* (_optique ondulatoire_), émet des **rayons lumineux** (_optique des rayons_), émet des *photons* (_optique quantique_) qui **divergent à partir de la source ponctuelle**. - -* **Faisceau lumineux** issu du point source : partie de la *__lumière émise par une source ponctuelle__* qui *intercepte un système optique* ou *passe à travers un diaphragme* limitant l'ouverture du faisceau. - - -* **voir à l'oeil nu** = **vision directe** d'un objet : les *faisceaux* de tous les points source visible de l'objet *interceptent la pupille de mon oeil*. - -![](vision-object-b.jpg)
-Fig. 1. Vision directe : les faisceaux de tous les points source visibles de l'objet interceptent la pupille de mon oeil. - -#### Image optique - -* L'objet est vu sous un **angle de vue**, dont la direction principale nommée **ligne de visée** définit (_lorsque orienté positivement dans le sens de la lumière incidente_) l'**axe optique** du système imageur. - -* Le *faisceau lumineux issu et divergent de chaque point source* de l'objet et qui intercepte le système imageur, après interaction *converge vers un nouveau point* de l'espace appelé **point image réel**, ou *diverge à partir d'un nouveau point* de l'espace appelé **point image virtuel**. - -* **Image** : *ensemble de tous les points réels et virtuels*. - -* **cohérence de forme** entre objet initial et son image, mais des *distorsions de forme peuvent apparaître*. - -![](vision-image.jpg)
-Fig. 2a. Vision d'une image : un imageur (rectangle) a modifié les faisceaux incidents issu des points sources. Seuls les faisceaux issus des points images entrent dans mon oeil. Ici les points image sont réels. - -![](image-virtuelle.jpg)
-Fig. 2b. Ici les points image sont virtuels. - -#### Imageur optique, principes physiques de base - -** Imageur** : -* **intercepte une partie de la lumière** émise ou diffusée par l'objet physique. -* *modifie le faisceau* de lumière issu de chaque source ponctuelle, en un **nouveau faisceau** qui :
-\- *converge* en un autre point de l'espace $\Longrightarrow$ *concentration d'énergie lumineuse* en ce point.
-\- *diverge* à partir d'un autre point de l'espace $\Longrightarrow$ *pas de concentration d'énergie lumineuse* en ce point. - -**Imageur optique** : -* créé une *image* en **vraies trois dimensions** de la surface orientée vers l'imageur de l'object étendu. -* utilise les phénomènes de **réfraction et/ou réflexion**. - -* peut être : un **élément optique simple mince** ou un **système optique centré** - -![](vision-object-image-2.jpg)
-Fig. 3a. En utilisant les phénomènes de réfraction et réflexion, un imageur optique modifie les faisceaux incidents issus de chaque point source, pour donner des faisceaux émergents qui concentrent réellement l'énergie lumineuse des points source en des points images réelles, ou qui divergent à partir de points image virtuels. Ici une image réelle est observée. - -![](Object-image_virtual.jpg) -Fig. 3b. Ici une image virtuelle est observée. - -#### Element optique simple mince - -* souvent possède une **symétrie de révolution autour d'un axe**.
- -![](sym_rev_2.gif)
-Fig. 4. Elément optique mince simple : élément réfractant ou réfléchissant, présentant une symétrie de révolution autour d'un axe. - -* **Mince** $\Longrightarrow$ *diamètre $\gg$ épaisseur ou profondeur*. - -* **Simple** : surfaces des éléments optiques *simples* sont *planes ou s'inscrivent dans une sphère.* - -* **Elements optiques simples minces** étudiés seront :
-\- *dioptres plans* ou *dioptres sphériques minces*.
-\- *miroirs plans* ou *miroirs sphériques minces*.
-\- *lentilles minces*. - -#### Système optique centré - -* **Combinaison** *d'éléments optiques simples minces* **centrés** *sur un axe de révolution commun* qui devient l'axe optique du système (_quand orienté positivement dans la direction de la lumière incidente sur le système)._ - -* *Intérêt* : peut être **caractérisé comme un tout**. - -![](axe_opt.gif)
-Fig. 5. Système optique centré : combinaison d'éléments optiques simples minces centrés sur un axe de révolution commun. - -### Quel cadre physique pour décrire l'imagerie optique ? - -#### De l'idéalisation mathématique à la réalité physique. - -* **Point** : concept mathématique de point mathematical.
-a une *position* dans l'espace, mais *pas d'extension*, *pas de volume*, *pas d'orientation*. - -* **Point image** signification physique : Le faisceau émergent d'un imageur converge (point image réel) ou semble diverger (point image virtuel) d'un volume de dans l'espace si petit que son *extension peut être négligée*, parce que :
-\- l'extension de son volume ne peut être résolue à l'oeil nu.
-\- la surface illuminée est inférieure au pixel d'un capteur d'image. - - - -* **système optique stigmatique** : *donne un point image à chaque point objet* (**n'existe pas**). - -* **système optique quasi-stigmatique** : *dans certaines conditions d'utilisation* un élément ou un système optique peut devenir **presque stigmatique** = **quasi-stigmatique** et s'appeler *imageurs*. - -* **Imageur optique** = **élément ou système optique quasi-stigmatique** utilisé pour la formation d'images. - - - -#### Cadre de l'approximation paraxiale de l'optique des rayons. - -* Nous utilisons le concept de **rayon lumineux**, base de *l'optique des rayons* - -* **optique des rayons** = **optique géométrique** - -* Quand les *systèmes optiques sont considérés comme stigmatiques*, leur étude est réalisée dans le cadre de l'**approximation paraxiale de l'optique des rayons**. - -* **Optique paraxiale des rayons** = *approximation paraxiale de l'optique des rayons* = *approximation paraxiale de l'optique géométrique* - -* Un *faisceau qui diverge d'une source ponctuelle*, est modifié par un imageur et après émergence, *converge à nouveau vers un point image réel* ou *diverge depuis un point image virtuel*.

-  Ã©quivalent à

-\- *tous les rayons issus d'un point source* sont déviés par l'imageur et *se croisent à nouveau au point image réel conjugué*, ou *leurs prolongements se croisent au point image virtuelle conjugué*.

-$\Longrightarrow$ la **connaissance de seulement deux rayons différents** issus du même point source et traversant l'imageur **est suffisante** pour déterminer la position du point image conjugué. - -* Pour toute source ponctuelle et pour tout imageur, les **trajectoires de 3 rayons particuliers seront spécifiées.**. - -![](imagerie-rays-optics.gif)
-Fig. 6a. Optique des rayons lumineux : 3 rayons particuliers sont spécifiés (2 sont suffisants) qui permettent de localiser le point image de tout point objet. Sur cette figure, l'imageur est une lentille mince convergente, et pour cette position de l'objet, l'image obtenue est réelle. - -![](imagerie-rays-optics-image-virtual.gif)
-Fig. 6b. Sur cette figure, l'imageur est une lentille mince divergente, et pour cette position de l'objet, l'image obtenue est virtuelle. - -### Comment est modélisé et caractérisé un élement optique simple mince en optique paraxiale des rayons ? - -#### Element optique simple mince - -* **Element optique simple mince** = élément optique dont *l'épaisseur peut être négligée devant son diamètre* **$\Longrightarrow$ représenté par un plan (Elt)**. - -* Element optique simple mince* possèdent une **symétrie de révolution autour d'un axe** :
-$\Longrightarrow$ mêm comprtement optique dans tout plan contenant l'axe de symétrie.
-$\Longrightarrow$ *source ponctuelle et point image conjugué appartiennent à un même plan qui contient l'axe de symétrie.
-$\Longrightarrow$ travailler dans la **vue en coupe** correspondant à ce plan est **suffisant**. - -* **Représentation** dans une vue en coupe contenant l'axe de symétrie : *sègment de droite [Elt] perpendiculaire à l'axe optique*. - -* *Localisation* avec son **sommet S** : intersection de [Elt] avec l'axe optique. - -#### Comportement optique - -* \- A chaque source ponctuelle B correspond un unique point image B'.
-\- A chaque point image B 'correspond un point source unique B :
-$\Longrightarrow$ **B et B' sont des points conjugués**. - -![](objeto-imagen-bb.jpg)
-Fig. 7a. Le faisceau incident sur l'élément optique est issu d'une source ponctuelle B. Ici, le faisceau correspondant émergent de l'élément optique converge vers un point image B' qui est un point image réel, parce que l'énergie lumineuse du faisceau émergent en concentrée en B'. - -![](object-image-conjugate-virtual.jpg)
-Fig. 7b. Le faisceau incident sur l'élément optique est issu d'une source ponctuelle B. Ici, le faisceau correspondant émergent de l'élément optique diverge encore. Mais son prolongement montre qu'il diverge à partir d'un point image B' qui est un point image virtuel, parce que l'énergie lumineuse de ce faisceau émergent continue de se disperser dans l'espace : pas de concentration de cette énergie en B'. - -* Toutes les sources ponctuelles (A ; B, C, ...) appartenant à un même plan object (PO) perpendiculaire à l'axe optique ont des points image conjugés (A' ; B', C', ...) situés dans un même plan image (PI) perpendiculaire à l'axe optique :
-$\Longrightarrow$ **(PO) et (PI) sont des plans conjugués**. -![](plano-objeto-plan-image-bb.jpg)
-Fig. 8. - -#### Coordonnées pour localiser les points objet et image - -* Chaque point (objet et image) est *projeté perpendiculairement sur l'axe optique* :
-\- souce ponctuelle B $\Longrightarrow$ point A sur l'axe optique.
-\- point image conjugué B' $\Longrightarrow$ point A' sur l'axe optique.
- -* *Distance d'un point à l'imageur optique* : **distance algébrique entre le sommet de l'imageur et la projection du point**.
- \- distance de la source ponctuelle B à l'imageur [Elt] : **$\overline{SA}$**
-\- distance du point image conjugué B' à l'imageur [Elt] : **$\overline{SA'}$** - -* *Distance d'un point par rapport à l'axe optique* : **distance algébrique entre la projection du point et le point lui-même**.
- \- distance de la source ponctuelle à l'axe optique : **$\overline{AB}$**
-\- distance du point image conjugué à l'axe optique : **$\overline{A'B'}$** - -![](objeto-imagen-posicion-tamano-bb.jpg)
Fig. 9a. - -![](object-image-plan-conjugate-virtual.jpg)
Fig. 9b. - -#### Caractérisation d'un élément optique simple mince - -**4 points ** *localisés sur l'axe optique* caractérisent le comportement optique : **S , C, F' and F** - -* **S** : **sommet** de l'imageur mince : *indique sa position* dans l'espace, et sur l'axe optique. -* **C** : **point nodal** : par définition *tous les rayons* (ou leurs prolongements) qui *passent par le point nodal C* ne sont *pas déviés* lors de la traversée de l'élément optique. Position caractérisés par sa distance algébrique au sommet S : $\overline{SC}$.
-Le *point nodal* est un *centre* (_dont la signification physique exacte dépend du type d'élement optique simple mince._) - -* **F'** : **point focal image** : tous les *rayons incidents* (ou leurs prolongement) *parallèles à l'axe optique* *après traversée* de l'imageur mince, *passent par F'*. -* **F** : **point focal objet** : tous les *rayons incidents* (ou leurs prolongement) *passant par F , ressortent** de l'imageur *parallèles à l'axe optique*. - -qui définissent **3 plans importants, perpendiculaires à l'axe optique** - -* **(Elt)** : représentation de **l'imageur miçnce, contient S** : les *rayons incidents changent de direction à la traversée de (Elt)*. -* **(P')** : **plan focal image, contient F'** : *tous les rayons incidents parallèles entre eux* issus d'une source ponctuelle à l'infini *quittent (Elt) pour converger* (ou leurs prolongements) *en un point image B' appartenant à (P')*. Localisation de B' dans (P') : *intersection du rayon passant par C avec (P')*. -* **(P)** : **plan focal objet, contient F** : *tous les rayons incidents provenant d'une même source ponctuelle B quittent (Elt) parallèles entre eux*, donnant un point image B' localisé à l'infini, *dans la direction du rayon passant par C*. - -et **2 importantes distances algébriques** - -* **$f'=\overline{SF'}$** : *distance algébrique entre l'imageur mince (Elt) et le plan focal image (P')* :
- -* **$f=\overline{SF}$** : *distance algébrique entre l'imageur mince (Elt) et le plan focal objet (P)* :
- - -### Significations importantes des plans focaux - -#### Plan focal image : - -* *Sens physique* :
**objet B à l'infini $\Longleftrightarrow |\overline{SB}| \ll |f|$**. - -* **Objet à l'infini $\Longleftrightarrow$ image dans (P')**, **visible à l'oeil nu** que l'élément optique soit convergent ou divergent. - - -![](plano-imagen-real-convergencia-bb.jpg)
-Fig. 10. Exemple : vision directe du ciel étoilé à travers un télescope. Un télescope n'est pas un imageur mince, mais la définition du plan focal image est la même). - -* **Object at infinity $\Longleftrightarrow$ ilmage dans (P')**, peut être **capturée par un capteur d'image** *seulement si l'élément optique est convergent (pour avoir une image réelle dans ce cas). - -![](plano-imagen-real-convergencia-pantalla-bb.jpg)
-Fig. 11. Exemple : photo prise avec un téléobjectif (un téléobjectif n'est pas un imageur mince, mais la définition du plan focal image est la même). - -#### Plan focal object (P) - -* *Sens physique* :
**image B' à l'infini $\Longleftrightarrow |\overline{SB'}| \ll |f'|$**. - -* **Object dans (P) $\Longleftrightarrow$ image à l'infini** - -![](plano-objeto-fisico-bb.jpg)
-Fig. 12. Exemples : l'objet peut être l'ampoule d'un phare, ou la pellicule d'un film dans un projecteur de cinéma non numérique (faisceaux émergents quasi-parallèles pour éclairer devant et loin dans les deux cas). - -### Comment déterminer l'image donnée par un élément optique simple mince? - -#### Etude graphique - -##### Deux échelles différentes - -* Objet et image : *tailles transverses $|\overline{AB}|$, $|\overline{A'B'}\;\;\ll$ distances par rapport à l'élément optique* le long de l'axe optique $|\overline{SA}|$ , $|\overline{SA'}|$.
-$\Longrightarrow$ dimensions perpendiculaires à l'axe optique $\ll$ dimensions le long de l'axe optique. - -* Donc **Etude graphique précise** $\Longrightarrow$ *dilater fortement l'échelle pour les mesures de distances perpendiculaires à l'axe optique*. - -![](objeto-imagen-posicion-tamano-bb.jpg)
-Fig. 13. - -##### Déterminer les points conjugués - -D'un point donné (objet ou image) **3 rayons de lumières spécifiques peuvent être tracés** (2 seulement sont nécessaires), dont l*intersection* (ou l'intersection de leurs prolongements) *donne le point conjugué* : - -![](objeto-imagen-3-rayos-bb.jpg) -Fig. 14. - -* **[Ray1]** : Rayons incidents (ou leurs prolongements) passant à travers le foyer objet F quittent (ou leurs prolongements) l'imageur parallèlement à l'axe optique. -* **[Ray2]** : Rayons incidents (ou leurs prolongements) parallèles à l'axe optique ressortent de l'imageur en passant (les rayons ou leurs prolongements) par le foyer image F'. -* **[Ray3]** : Rayons incidents passant par le point nodal C ne changent pas de direction en émergent de l'imageur. - -##### Conséquences des définitions des points focaux - -* Les **rayons incidents parallèles entre eux** (ou leurs prolongements) se croisent en un *même point du plan focal image* (P').
-(localisation : intersection de (P') avec [Ray3]) - -* Les **rayons émergents parallèles entre eux** (ou leurs prolongements) divergent d'une *même source ponctuelle située dans le plan focal objet* (P).
-(localisation : intersection de (P) avec [Ray3]) - - -##### Déterminer le rayon émergent correspondant à un rayon incident quelconque. - -* **déviation d'un rayon lumineux par une élement optique mince** : *interaction locale au point d'impact* (réfraction or réflexion) entre le rayon incident et l'élément optique mince $\Longrightarrow$ *indépendent de la distance de la source ponctuelle à l'origine du rayon incident*. - -* Si le rayon incident quelconque était émis par une**source ponctuelle B à l'infini** $\Longrightarrow$ le point image conjugué *B' serait dans le plan focal image (P')*. - -* le **rayon issu de B** (à l'infini) **passant par le point C** *ne change pas de direction* $\Longrightarrow$ *localisation de B' dans (P')*. - -* Le **rayon émergent** (ou son prolongement) correspondant au rayon incident quelconque = *ligne droite entre le point d'impact et B'*. - -![](rayon-incident-quelconque-5.gif)
-Fig. 15. - -##### Déterminer le rayon incident correspondant à un rayon émergent quelconque - -* **déviation d'un rayon lumineux par une élement optique mince** : *interaction locale au point d'impact* (réfraction or réflexion) entre le rayon incident et l'élément optique mince $\Longrightarrow$ *indépendent de la distance au point image*. - -* Si le rayon émergent quelconque participait à un **point image B' à l'infini** $\Longrightarrow$ la source ponctuelle conjugués *B serait dans le plan focal objet (P)*. - -* Le **rayon émergent vers B'** (à l'infini) **passant par le point nodal C** ne change ps de direction* $\Longrightarrow$ *location de B dans (P)*. - -* **rayon incident** correspondant (ou son prolongement) = *ligne droite entre le point d'impact et B*. - - -#### Etude analytique - -##### Distance d'un point conjugué à l'élément optique mince - -* déduite à partir de la **relation de conjugaison** de l'élement optique mince. - -* seront donnés les relations de conjugaisons pour:
-\- *miroir sphérique mince*
-\- *dioptre sphérique mince*
-\- *lentille mince*
-(relations démontrées au niveau contreforts) - -##### Distance d'un point conjugué à l'axe optique - -* déduite à partir du **grandissement transverse $\gamma_T$**. - -* **Définition** : **$\gamma_T=\dfrac{\overline{A'B'}}{\overline{A'B'}}$** - -* **$\gamma_T>0$** *$\Longleftrightarrow$* **image droite**
- **$\gamma_T<0$** *$\Longleftrightarrow$* **image inversée** - -* **Expression** : *dépends du* type d' *élément optique simple* :
-Seront données les expressions pour :
-\- *miroir sphérique mince*
-\- *dioptre sphérique mince*
-\- *lentille mince*
-(relations démontrées au niveau contreforts) - -* **valeur algébrique de $\gamma_T$** : est une *fonction de $\overline{AB}$ et $\overline{A'B'}$*
-$\Longrightarrow$ dépends de la position des points conjugués
-$\Longrightarrow$ **ne caractérise pas l'élement optique** lui-même. - -### Comment caractériser l'action d'un imageur ? - -#### Caractériser un objet étendu - -* Object étendu [AB] or [B$_1$B$_2$], **perpendiculairement à l'axe optique** :

-\- caractérisé par sa *taille algébrique transverse* (distance entre ses extrémités) : **$\overline{AB}$** ou **$\overline{B_1B_2}$**

-\- ou caractérisé par l'*angle apparent* (en valeur algébrique ou non) *sous lequel l'objet est vu depuis le point nodal* de l'oeil (vision directe) ou de l'imageur mince : **$\alpha$** ou **$\overline{\alpha}$** - -* Object étendu [A$_1$A$_2$] **le long de l'axe optique** :

-caractérisé par sa *taille algébrique longitudinale* (distance entre ses extrémités) : **$\overline{A_1A_2}$** - -#### caractérisation de l'image étendue conjuguée - -* Image étendue [A'B'] or [B'$_1$B'$_2$], **perpendiculairement à l'axe optique** :

-\- caractérisée par sa *taille algébrique* (distance entre ses extrémités) : **$\overline{A'B'}$** ou **$\overline{B_1'B_2'}$**

-\- ou caractérisée par l'*angle apparent* (en valeur algébrique ou non) *sous lequel l'objet est vu depuis le point nodal* de l'oeil (vision directe) ou de l'imageur mince : **$\alpha$** or **$\overline{\alpha}$** - -* Image étendue [A'$_1$A'$_2$] **le long de l'axe optique** :

-caractérisée par sa *taille algébrique* (distance entre ses extrémités) : **$\overline{A'_1A'_2}$** - -#### Caractériser l'action d'un imageur sur un objet étendu - -L'imageur donne une image d'un objet. La **caractérisation de l'action de l'imageur** dépend de *comment sont caractérisés l'objet et l'image*. - -##### Grandissement transverse d'un objet étendu - -* *Objet et image* sont tous deux **caractérisés par leur taille algébriques transverses** :
-**$\Longrightarrow$** *action de l'imageur* caractérisée par **grandissement transverse $\gamma_T$**

-**$\gamma_T=\dfrac{image\:size}{objet\:size}=\dfrac{\overline{A'B'}}{\overline{AB}}$** - -##### Grossissement d'un objet étendu - -* *Objet et image* sont tous deux **caractérisés par leur angle apparent** :
-**$\Longrightarrow$** *action de l'imageur* caractérisée par le **grossissement $G$**

- -**$G=\dfrac{image\:apparent\:angle}{objet\:apparent\:angle}=\dfrac{\overline{ \alpha'}}{\overline{ \alpha }}$**

-ou $G=\pm\dfrac{ \alpha'}{ \alpha }$, avec signe + si image droite, signe - si image inversée.

- -![](apparent-magnitude-magnifying-glass-1018.gif)
-Fig. 16. Dans cette expérience, l'objet observé est situé à une certaine distance de la loupe, ainsi que l'oeil de l'observateur. Pour ces conditions d'utilisation, la loupe donne un grossissement de +2.5. Il y a des conditions d'utilisation optimum de la loupe (voir chapitre "instruments optiques"). - -!!!! *ATTENTION*
-!!!! Un angle apparent sous lequel est vu un objet ou une image dépend de la distance entre l'objet ou l'image et le point nodal du système observateur (oeil humain, ou objectif d'un appareil photo par exemple) $\Longrightarrow$ Il faudra définir plus précisément l'angle apparent (voir chapitre "instruments optiques"). - -##### Grandissement longitudinal d'un objet étendu - -* *Objet et image* sont tous deux **caractérisés par leur taille algébrique longitudinale** :
-**$\Longrightarrow$** *action de l'imageur* caractérisée par le **grandissement longitudinal $\gamma_L$**

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