#SMMS
Objective : Measure displacement field, and obtain the strain field.

Need markings, but is often kind to the material, and the measure itself does not need any physical contact with the material. => Useful for hostile environments.
However light is not always reliable (for example heat can bend the path of the light)

In addition to that, they are multi-scale methods. Depending on the optic tools, measures can be taken at the micron or tens of kilometers scale.

## Vocabulary

 The **test body** *(corp d'épreuve)* is the body being tested.

The **resolution** is the smallest change detected that is not considered "noise", the detection threshold.

The **sensitivity** *(sensibilité)* is how much the response of the sensor change when the measured physical quantity changes.

**Accuracy** *(précision)* is banned (ISO 5725-1), and are preferred **trueness** *(justesse)* and **precision** *(fidélité)*.

![[Trueness vs Precision]]

## Sensing light

Light sensors measure the photon flux, and therefore work only with grayscale. 

They cannot measure it on the full surface of the sensor, with the upper bound being 95% of photosensitive surface 

To measure color, a filter is applied and the photon flux assessed for this color specifically. But doing this for R, G, and B you can get a full color image, at the cost of the information (discontinuities in the red light between to R sensors are not measured for example). 
![[Bayer_pattern_on_sensor.svg]]

(image of a Bayer matrix)

You can also use mirrors to not lose so much informations, but it is rarely used in practice.

Whatever the architecture, one of two types of sensor is used :
#### CCD : the ol' reliable

Used to be the only viable option, and is very precise, but slow and power-hungry.

#### CMOS : quick and dirty

The newcomer, faster and energy-efficient but less precise.


# Philosophy

Care needs to be taken regarding what you measure :
you cannot measure force directly, so if you want force you have to take hypothesis for a method to get the force.

In calculus, often everything is assumed to be continuous, but it often lacks real meaning, and continuity cannot be measured. Each sensor has its own **resolution**.

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# Local Approach (2d)

Difference in the sense of least squares : 
$$C(\overline{x,y},\overline{u,v})=\sum_{i,j=-n/2}^{n/2}[I\overline{(x+i,y+j)}-I^*\overline{(x+u+i,y+v+j)}]^2$$
$I$ Image before displacement, $I^*$ Image after displacement
$i$,$j$ coordinate within the subset

Other coefficients can be calculated, for example the correlation product, which is roughly a [convolution](https://www.youtube.com/watch?v=KuXjwB4LzSA&pp=ygULY29udm9sdXRpb24%3D). It is the coefficient used in fluid mechanics because it can be efficiently computed with the FFT.

The subset size is always a compromise : a small subset allows for more local information with more noise, while a large subset allows for global informations with less noise.

## A word of caution

The study body's surface must be plane, and the camera axis normal to this plane. And any out-of-plane displacement causes errors. 

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# Volumetric Correlation

The goal is to be able to see the heterogeneity of the material, and get the structural architecture.  (even get architecture gradients)

### Tomography

aka volumetric scan, like IRM, X ray scan, ultrasonic scans

-> sinogram

To get the image of the internal structure, the inverse transform of Radon is used.

**Issue** : when you need to load the study body : loading equipment may be bulky and not fit in the tomograph.

The texture used for the process is often the microstructure itself, so it is  impossible to access to the behavior of the microstructure (since 2 colors are 2 different materials).

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# Computing parameters

Usually to fully characterize a material, a lot of test need to be conducted. One of the goals of Photomechanics it to find a reliable way of finding a lot of parameters from a few tests (even if more complicated).
### FEMU
It is an iterative parameter tweaking. An intuitive method, a bit rustic but works in most cases.
(another field but perfectly describes the method : [video](https://www.youtube.com/watch?v=IHZwWFHWa-w)*20min*)

### Other methods
Can need some conditions to work :
##### Kinematic admissibility :
$$\varepsilon = \frac{\nabla U+\nabla U^T}{2},\ x \in B$$
(see [video](https://www.youtube.com/watch?v=X-H3Fwdm-kI) *10min*)
$$U=U_d,\ x\in\delta B $$
($\delta B$ is the boundary of the body $B$)
##### Static admissibility
$$\nabla \cdot \sigma + f = \rho \gamma$$
*(I may be wrong but I see a generalization of $F=ma$)
$$\sigma n=T$$

(for other definitions of admissibility see [article](https://en.wikiversity.org/wiki/Elasticity/Kinematic_admissibility))

## A word of caution
$\varepsilon$ is computed from deriving $U$, adding a lot of noise to the measures. To have better result it is more rigorous to use $U$, even if it means struggling with boundary conditions.