Linear Grating Scale Basics: Everything You Need to Know | MachineMFG

Linear Grating Scale Basics: Everything You Need to Know


Structure and Working Principle of Grating.

1. Structure of Grating


Grating – many small stripes (engraved lines) of equal distance and alternating brightness and darkness are uniformly engraved on a coated glass surface.

a – is the width of the grating lines (non-transparent)

b – is the space width between grating lines (transparent)

a+b=W grating pitch (also known as grating constant)

Usually, a=b=W/2, but it can also be engraved as a:b=1.1:0.9.

Commonly used gratings are engraved with 10, 25, 50, 100, or 250 lines per millimeter.

2. Measurement Principle of Grating

Measurement Principle of Grating

Moire Fringes – When two equal-pitch gratings (Grating 1 and Grating 2) are overlaid face to face, leaving a small gap in the middle, and the small grating angle θ is formed between the two grating lines, alternating bright and dark stripes appear in the direction close to the vertical grating line.

On the d-d line, the two grating lines overlap, and the transparent area is the largest, forming the bright band of the stripe- consisting of a series of rhombus patterns.

On the f-f line, the two grating lines are offset, forming the dark band of the stripe- consisting of some black cross-line patterns.

Moire fringe displacement measurement has the following three characteristics:

(1) Amplification effect of displacement

Stripe width BH – when the grating moves forward or backward by one grating pitch, the Moire fringes move forward or backward by one stripe width.

The Relationship between BH and θ:

As θ decreases, BH increases. Therefore, W is amplified by 1/θ. For example, when θ=0.1°, 1/θ=573, meaning that BH is 573 times the grating pitch W. This means that the grating has a displacement amplification effect, thereby increasing the sensitivity of the measurement.

(2) Direction of Moire Fringe Movement

Direction of Moire Fringe Movement

When Grating 1 moves to the right along the cutting line in a vertical direction, Moiré fringes move upwards along Grating 2’s grid lines. On the other hand, when Grating 1 moves to the left, Moiré fringes move downwards along Grating 2’s grid lines. Therefore, the direction of Grating 1’s movement can be identified as the direction of Moiré fringe movement →.

(3) The Average Effect of Error

Moiré fringes are formed by the large number of engraved lines on a grating, and they have a counteractive effect on the engraved error of the lines. This effect can significantly reduce the influence of short-period errors.

Moiré fringes are formed by the light-blocking and transmitting effects between two gratings.
Moiré fringes are formed by the light-blocking and transmitting effects between two gratings.

Composition of Grating Sensors

Composition of Grating Sensors

Grating Readhead: Utilizes the principle of gratings to convert the input quantity (displacement) into a corresponding electrical signal.

Components: Ruler grating, indicator grating, optical pathway system, photoelectric elements, etc.

Grating Digital Display: To discern the direction of displacement, increase measurement precision, and enable digital display, the output signal from the grating readhead must be converted into a digital signal.

Components: Shaping amplification circuit, subdivision circuit, directional discrimination circuit, and digital display circuit, etc.

Structure of Enclosed Grating Ruler

Structure of Enclosed Grating Ruler

The grating ruler consists of a fixed scale body and a movable readout head.

The fixed scale body is an aluminum casing designed to protect the ruler, scanning unit, and guide rails inside from damage caused by chips, dust, or splashing water.

The movable readout head consists of a scanning unit, a precision connector, and an installation block. The precision connector connects the scanning unit to the installation block, which compensates for small mechanical errors in the guide rails.

Function and Advantages of the Grating Ruler

The linear grating ruler is used to measure the position of linear axis movement. As it directly measures the mechanical position, it can accurately reflect the actual position of the machine tool.

Function and Advantages of the Grating Ruler

By using the linear grating ruler to measure the position of the slide, the position control loop includes all feeding mechanisms. This is the closed-loop control mode. The mechanical motion error is detected by the linear grating ruler in the sliding plate and corrected by the control system circuitry.

Therefore, it can eliminate potential errors from multiple sources:

  • Positioning error caused by the temperature characteristics of the ball screw and guide rails
  • Reverse error of ball screw
  • Motion characteristic error caused by pitch error of the ball screw

Applications of Grating Rulers

Processing equipment: lathes, milling machines, boring machines, grinders, drilling machines, EDM machines, wire cutting, machining centers, etc.

Measurement instruments: projectors, image measuring instruments, tool microscopes, etc.

It can also compensate for errors in tool movement on CNC machine tools

Equipped with PLC for displacement measurement in various automated mechanisms.

Measurement Principle of the Grating Ruler

Incremental grating ruler

The measurement principle of the incremental grating ruler is to modulate the light through two mutually moving gratings into Moiré fringes. By counting and subdividing the Moiré fringes, the displacement change is obtained. The absolute position is determined by setting one or more reference points on the scale grating.

Measurement Principle of the Grating Ruler


The grating ruler has advantages such as a simple structure, long mechanical lifespan, high reliability, strong anti-interference capability, long transmission distance, high accuracy, and low cost.

However, incremental grating sensors also have shortcomings. Incremental grating rulers can only output the relative position of the shaft rotation.

The reference point must be set every time the power is turned off or restarted, and there is some subdivision error in the signal processing method.

Absolute grating ruler

The measurement principle of the absolute grating ruler is to directly encode the absolute position data in the form of codes on the grating by flickering grating lines at different widths and spacing on the grating ruler.

The subsequent electronic equipment can obtain position information while the grating ruler is powered.

Absolute grating ruler


The current position information can be obtained directly after power-on without the need for a “zeroing” operation, simplifying the control system design. Absolute position calculation is completed in the readout head without the need for subsequent subdivision circuits. The use of bidirectional serial communication technology ensures reliable communication.

Reference Point Types

The absolute position of the grating ruler is determined using reference markers (zero positions).

To shorten the distance to return to the zero position, Heidenhain designed distance-coded reference markers within the measurement length.

The absolute position of the grating ruler can be determined each time two reference markers (with a distance determined by mathematical algorithms) are passed.

Encoders with distance-coded reference points have the letter “C” after the model number (for example, LS 487C).

Single reference point

Single reference point

Equidistant reference points.

Equidistant reference points

Distance-coded reference point/C-type.

Distance-coded reference point/C-type
 Signal cyclenominal increment numbermaximum displacement distance
LF4μm500020 mm
LS20μm100020 mm
LB40μm200080 mm

Non-referenced absolute linear scale

Non-referenced absolute linear scale

Signal Classification of Linear Scales

Absolute signal: Endat, Fanuc serial, Siemens, Mitsubishi, Panasonic, etc.

Incremental signal: Sine wave signal (1-Vpp signal), square wave signal (TTL signal).

Signal Classification of Linear Scales

Technical Specifications of Linear Scales

1. Grating pitch:

The linear scale outputs electrical signals, and grating pitch refers to the physical grating lines on the linear scale. Every time the linear scale moves a distance equal to the grating pitch, the output electrical signal changes one cycle.

Example: When the grating pitch is 20um, if the linear scale moves a distance of 20um, the linear scale will output a sine wave with 360° phase shift and two-phase difference of 90°.

2. Signal cycle:

With the development of measuring technology, it is now possible to use frequency multiplication circuits on the linear scale reading head to multiply the sine wave generated by each grating line signal.

Therefore, the signal output cycle of the linear scale can be refined. The signal after being multiplied by the reading head is much denser than the original grating line signal, and the length of the densified signal is called the signal cycle.

If the reading head does not have frequency multiplication capability, then the grating pitch equals the signal cycle.

3. Frequency multiplication:

Frequency multiplication can be understood as densifying the original signal. Frequency multiplication can shorten the period of a sine wave, shorten the measured distance corresponding to each period, and improve the measuring accuracy.

The common frequency multiplication methods include: reading head frequency multiplication, post-multiplication instruments (provided by linear scale manufacturers, similar to preamplifiers, used for signal amplification and frequency multiplication), frequency multiplication of CNC systems, etc.

4. Measurement step:

Sine wave signals that have gone through frequency multiplication are used to measure position. Due to limitations in the manufacturing process, error level, and processing capability of the position recording circuit of the linear scale, it is impossible to infinitely multiply the original grating pitch signal.

Therefore, linear scale manufacturers have a recommended measurement step for each type of linear scale. This value refers to the minimum measured distance that the linear scale can tolerate. Within this measurement step range, the nominal measuring accuracy of the linear scale can be achieved.

Compared to CNC systems, this measurement step is usually the minimum instruction unit of the system. Similarly, this technical specification also specifies the measuring accuracy (resolution) of the linear scale.

5. Resolution:

Measuring accuracy refers to the minimum length change that the linear scale can read and output, such as 5um, 1um, 0.5um, 0.1um.

6. Measurement accuracy:

Measurement accuracy refers to the accuracy of the signal data output by the linear scale to the true length being measured.

Position error within the entire measurement range: If the maximum value of the position error established on the basis of the average value within any 1m long measurement range falls within ±a, then ±a um is the accuracy level.

In closed linear scales, this data reflects the accuracy of the linear scale, including the reading head, i.e., system accuracy. (Heidenhain: ±0.1, ±0.2, ±0.5, ±1, ±2, ±3, ±5, ±10, ±15um)

Position error within a single signal cycle:

The position deviation within a single signal cycle is determined by the grating quality, scanning quality, and signal cycle of the linear scale. The position error within a single signal cycle is usually within the range of ±2% to ±0.5% of the signal cycle.

The smaller the signal cycle, the smaller the error within a single signal cycle. This is very important for positioning accuracy during slow motion and axis movement and speed control during axis movement, which determines the surface quality and quality of the processed parts.

 The signal cycle of the scanning signalThe maximum interpolation error within a single signal cycle
F L4μm0.08 μm
LC48120 μm0.4μm
LS20 μm04 μm
LB40 μm0.8μm

Factors to Consider When Selecting a Linear Scale

  • Measuring length.
  • Signal interface: 1Vpp, TTL, HTL, absolute linear scale.
  • Grating pitch.
  • Measuring speed.
  • Accuracy level and resolution.
  • Space for installation position.
  • Method of establishing reference points.

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