Project Design Document

Magneto-Optical Trap (MOT)

Michael Doris

December 7, 2018

Revision 1 : December 8, 2018 Revision 2 : December 17, 2018

Revision 3 : May 7, 2019

1. Architectural Design

a. Functional Elements

i. Turn On/Off Rubidium Oven ii. Turn On/Off MOT Coils

iii. Receive Power On/Off Signal iv. Receive Transition Reference Signal v. Send Frequency Locking Signal

vi. Receive Frequency Locking Signal vii. Frequency Lock Laser Output

viii. Send Red-Detune Cooling Beams Signal ix. Receive Red-Detune Cooling Beams Signal x. Detune Beam

xi. Develop Rubidium Particle Beam xii. Load Chamber

xiii. Open/Close xiv. Change Current xv. Open/Close Trap Shutters

xvi. Receive Open/Close Signal xvii. Open/Close Cooling Shutters

xviii. Begin Cooling Process via Experiment Configuration File xix. Open/Close Image Beam Shutters xx. Take Image Signal

xxi. Receive Image Signal xxii. Send Image Data Signal

xxiii. Receive Send Image Data Signal xxiv. Receive Image Data xxv. Take Image

xxvi. Send Image Data xxvii. Process Image Data

xxviii. Change MOT Coil Currents xxix. Receive Change Current Signal

b. Relationships

Physical Element Functional Element Labscript Controller Turn On/Off Rubidium Oven Turn On/Off MOT Coils Send Frequency Locking Signal Send Red-Detune Cooling Beams Signal Develop Rubidium Particle Beam Load Chamber Open/Close Trap Shutters Open/Close Cooling Shutters Begin Cooling Process via Experiment Configuration File Open/Close Image Beam Shutters Take Image Signal Send Image Data Signal Receive Image Data Process Image Data Change MOT Coil Currents

Anti-Helmholtz Coils Receive Power On/Off Signal Receive Change Current Signal Change Current Helmholtz Coils Receive Power On/Off Signal Receive Change Current Signal Change Current Shutters Receive Open/Close Signal Open/Close AOMs Receive Red-Detune Cooling Beams Signal Detune Beam Locking Controller Receive Frequency Locking Signal Frequency Lock Laser Output Camera Receive Image Signal Take Image Send Image Data

2. Hardware Design

a. MOT Coils i. Theory

This project uses two type of coil configurations. One Anti-Helmholtz coil for the main trapping and cooling magnetic fields, and one Helmholtz coil for the cancellation of Earth’s magnetic field with Shim coil magnetic fields. For the Anti-Helmholtz configuration, the current is moving in opposing directions through each coil. For the Helmholtz configuration, the current is moving in the same direction through each coil. The overall design process is similar for both, so this theory will cover the Anti-Helmholtz derivation. Application toward the Helmholtz configuration requires a simple flip in the sign of the current. The standard Anti-Helmholtz configuration is two coils sitting a distance apart that equals the length of radius of a single coil. The currents through each current are moving in opposite directions.

The field derivation will be skipped since it is simply the field from a current loop. This can be found trivially with a few minutes at some distance, r, from the plane of the loop on the z axis. The final field from a single wire loop is:

�� =��������

� �

2

1

��ℎ2

− ���

+ ������ �

���

The field from two coils sitting r (radius) in distance from each other is:

�� =��������

� �

2

⎣⎢⎢⎢⎢⎡

1

��ℎ2

− ���

+ ������ �

���

−1

��ℎ2

+ ���

+ ������ �

���

⎦⎥⎥⎥⎥⎤

Since the target magnetic field is known, this can be re-organized to solve for the required number of turns for a specific current through the two coils.

� =2

�������� �

��

⎣⎢⎢⎢⎢⎡

1

��ℎ2

− ���

+ ������ �

���

−1

��ℎ2

+ ���

+ ������ �

���

⎦⎥⎥⎥⎥⎤

The change of this field over a certain unit distance can then be found to be

��� =��������

� �

2

⎣⎢⎢⎢⎢⎡

3ℎ − 6�

2 ��ℎ2

− ���

+ ������ �

���

+3ℎ + 6�

2 ��ℎ2

+ ���

+ ������ �

���

⎦⎥⎥⎥⎥⎤

Which will be used to determine the configuration of the Anti-Helmholtz coil.

Now, these are rounded coils of copper wire, so they are essentially very large inductors. The amount of turns will influence the relative inductance and series resistance. The turns, inductance, and resistance will also in turn effect the switching time, generated back EMF, and heat output of the coils. For most calculations the radius of the coil is from the center of the coil to the geometrical center of the copper windings. The inductance of a coil can be found using:

� = ��������� �ln �8�����

������ − 2�

This inductance will in turn influence the decay time of the magnetic field, as well as the generated voltage spike when the coils are switched on or off. Before talking about the switching time, the possible voltage spike generated by a field switch off needs to be roughly calculated. This will influence the required voltage clamping of the protection circuitry, which will change the switch off time of the field.

������ = −���

��

Assuming an extremely short time span, this voltage could be extremely large. However, it's usually safe to assume a voltage spike of 4-5 times the supply voltage applied to the coil. To reduce the current, and by extension the magnetic field, in a controlled and timely manner you can set the clamp voltage and coil inductance such that the current dies over a certain time frame. The current decay can be found to be:

� = �� �1 − �

��

Where the time constant, τ, is defined by the clamp voltage, inductance, and steady state current. This gives us our approximate switching time of the coils.

� = ���

������

To find the series resistance you first need the total length of the wire,which can be found from the circumference of a single wire and the amount of turns.

� = 2�������

This in turn can be used to find the series resistance, which is the approximate resistance of the total length of copper wiring used.

������� =��

�������

Using this resistance you can calculate the power output of the coils.

� = ���������

The approximate heat output of the wiring per unit distance can be found using the specific heat of copper and the calculated power output. Note that this V is volume, not voltage.

� = �

���=

���

����

b. Schematics

Proposed Coil Circuit Equivalent

Coil Structure Prototype 1.

Coil Structure Prototype 2.

Final Coil Frame Design.

c. Laser System – ECDL i. Theory

The introduction of an external cavity and controlling electronics is a solution to the problems that free running diode lasers face and help stabilize and control the light that is emitted. The external cavity diode laser introduces four major components to further stabilize the cavity and operation of the laser: a collimating lens, a frequency selective optic such as a holographic grating, a piezo stack, and thermoelectric coolers. There exist many variations of the external cavity setup, but the two main configurations are the Littrow and Littman-Metcalf designs.

Possible ECDL Configurations. Image Source: Thorlabs

The Littrow design uses a single grating angled to select a specific wavelength of light and reflect the first order of it back into the laser. The zeroth order beam is reflected away from the grating according to the angle of incidence

.

Holographic Grating. Image Source: Thorlabs

Only light of the wavelength that satisfies the below equation will be reflected back into the laser.

2� sin � = ��

Here d is the inverse of the number of grooves per millimeter, theta is the angle of the

incident light, m is the order of light, and is the wavelength of light. Assuming a groove count of 1800 grooves/mm, first order light, and the required Rubidium transition wavelength of ~780 nm the grating angle comes out to be approximately 44.59

The downside to this configuration is that the zeroth order beam will move as the grating angle changes. This could be an issue in certain applications if beam alignment is critical. The Littman-Metcalf design solves this issue by introducing an additional mirror that acts as the frequency selecting optic. Light from the laser is reflected off the grating toward the mirror. This mirror then reflects the light back toward the grating at a certain angle, which selects for the frequency of light sent back into the laser. The light not reflected toward the mirror is used as the stationary output beam. Although this gives a stationary beam, it comes at a cost of power as the zeroth order beam is lost from the mirror. This project specifically went with the Littrow configuration for simplicity and maximum power.

A thermoelectric cooler is added beneath the laser head to stabilize and maintain a set temperature. As shown in section 1.4, the temperature of the diode laser influences the operating frequency of the internal cavity. This causes a sloping staircase like change in frequencies as temperature and current is changed. Most semiconductor lasers built for near IR wavelengths such as the 785 nm diodes used in this project have a wavelength change of approximately 0.31 nm/°C to reach a neighboring mode, and 0.02 nm/mA via current modulation in the currently selected mode. This suggests that a temperature change of about 16 degrees Celsius is enough to support a lasing wavelength of 780 nm. However, since multiple modes can exist within the cavity, only modes which exist at the peak of the gain curve will be emitted. When the diode is placed in an external cavity, the frequency selective grating allows the laser to amplify the desired mode. However, even with this temperature change the laser requires further stabilization to avoid random hopping to neighboring modes.

A piezo stack, or PZT, is placed behind the grating and allows fine tuning of the optics. A PZT is a perovskite material that changes in shape with an applied external electric field. For the PZT used in this project, a voltage of 0-150V is applied and allows a total length increase of 4.6 µm for a step size of 30.67 nm/V. The natural linewidth of the target Rubidium transition is about 6 MHz. This means any cavity change that results in a frequency shift of 3 MHz from the central frequency can cause a jump to another

neighboring transition. Using the equation below the wavelength change from this frequency change can be found to be 0.00609 pm.

∆� =Δ���

�

To correlate this change to the PZT’s displacement two factors must be accounted for. The grating angle that selects for the frequency fed back into the laser, and the cavity length that determines which modes can be supported. The wavelength change of 0.00609 pm can be found to correlate to an angle change of 4.40x10-7 degrees. With the use of basic trigonometry this angle change can be found to relate to a PZT displacement of 0.227 nm. Using the previously found step size of 30.67 nm/V it can be shown that an applied voltage change of 7.40 mV is sufficient enough to shift the frequency to another transition. However, changes in cavity length will also impact the supported modes of the laser. The modes that can exist within a cavity can be estimated with:

�� =��

2(�� + �)

Where l is the internal cavity length, L is the external cavity length, n is the active material’s index of refraction, and m is the mode order. Assuming a cavity length of 25 cm, and disregarding the internal cavity since the external cavity is much greater than the internal cavity length, the closest supported mode for 780 nm, or 384.349 THz, can be found to be 384.347 THz. Now if you solve for the change in cavity length, using a frequency shift of 3 MHz, the total PZT displacement can be shown to be 0.223 nm with an applied voltage change of 7.27 mV. The PZT influenced grating angle and external cavity length together influence the operating frequency of the ECDL. Since drive current and temperature modulation also influence the internal cavity, multiple combinations of current, temperature, and PZT voltage can exist to achieve specific transitions. A locking controller in combination with Saturation Spectroscopy can be used to find the correct settings and keep the ECDL at a set point.

ii. Schematics

d. Locking Controller i. Theory

The locking controller depends on three distinct parts to function correctly: Saturated Absorption Spectroscopy, the Sub-DAVLL locking method, and PID loops. These work together in tandem to produce a control signal that keeps a ECDL’s output from drifting away from a specific atomic transition.

To lock an ECDL saturated absorption spectroscopy must be employed to identify the transitions that exist within the target atom species and the required frequency to stimulate them. This method is also known as Doppler-free spectroscopy. Doppler broadening results from the velocity spread of atoms in a gas. This distribution follows the Maxwell-Boltzmann distribution.

�(�)�� = ���

2�����

����

�������

When laser light from the ECDL enters a gas such as Rubidium only those atoms near a velocity of zero will absorb a photon. Any atoms moving away from the beam will be red-shifted away from the absorption frequency, and any atoms moving toward the beam will be blue-shifted away from the absorption frequency. If this light exits the gas and is probed with a photodiode and oscilloscope, the resulting output resembles a Gaussian spread.

� = ���8�����2

���

This means that the accuracy of the probe will be limited by the Doppler broadened transition spectrum, and not the actual width of the transitions themselves. Essentially, the required transitions will be hidden out of sight and prevent setting the laser to the required frequency

To get around this limitation a pump-probe method is used. Instead of using a single probe beam to find the correct transition frequency, two beams are sent through the gas of atoms instead. A higher power pump beam saturates the atoms, preventing any further absorption of photons. A probe beam is then sent through in the opposite direction, bypassing the saturated zero-velocity atoms. When this beam hits a photodiode, it results in an output spike due to the lack of absorbed photons. An example of this is shown below, where the red line represents the Doppler broadened signal and the blue peaks represent the saturated absorption spectrum.

Example of Doppler Broadening with Saturation Absorption Peaks.

This then allows one to find a frequency and set the laser to that peak through a locking mechanism of some sort. For this project the locking scheme to be used will be the sub-doppler dichroic atomic vapor laser locking method. The Sub-DAVLL method is a hybrid between the standard DAVLL locking scheme and the hyperfine splitting of saturation absorption spectroscopy. The benefit to using this scheme is much more accurate locking signals that prevent even finer drifts. This method takes the same saturation absorption spectroscopy process, but now makes the probe and pump beam linearly polarized in a specific direction. An external magnetic field is applied in the direction of the probe beam propagation, which splits the hyperfine energy levels of the atoms. The doppler broadened signals and the sub doppler signals (the hyperfine transitions in blue in the figure above) are pushed further apart, and after the probe beam passes through the vapor cell, a wave plate and polarized beam splitting cube

are used to split out the circularly polarized absorption lines, + and -. This essentially makes two anti-symmetric hyperfine transition signals, and a background doppler broadened signal.

The + and - signals can then be fed into a difference amplifier to generate a process

variable for a PID loop. The resulting signal, if you’re on an atomic transition, will ideally be zero. Any deviation from this “zero” point will indicate a small drift from the desired transition. The output of the PID loop will then adjust the PZT controller settings accordingly to maintain that set point. PID loops are extremely common and well known controlling mechanisms, so I will only give a brief overview of the basics. Due to the slower nature of atomic drifts, the derivative control is not used in this project and a simple PI circuit suffices. The proportional gain produces an output that is proportional to the current error value, which is the difference between the set point and the process variable.

�(�) = ���(�)

The integral gain takes a sum of the error value over time, producing a value that is multiplied by the integral gain.

�(�) = �� � �(��)��′�

�

When combined with a proportional gain, it accumulates the remaining difference between the output and set point from the proportional gain, multiplies it by its own gain value, and adds it to the output to decrease the error.

�(�) = ���(�) + �� � �(��)��′�

�

Here u(t) represents the resulting output signal to the plant, or rather for this project, the PZT controller. This in turn changes the resulting ECDL output, which changes the signal generated from the sub-DAVLL locking scheme, and therefore changes the process variable value.

ii. Schematics

e. Shutters i. Theory

Laser shutters pass an input beam undisturbed in the open position, and dump the laser energy safely into the shutter body when in the closed position. These shutters generally take some waveform to trigger the open or closed position. For the shutters used in this project, an on or off signal can be generated through the use of 24V PWM or a simple 24V capacitor discharging circuit.

ii. Schematics

Initial Shutter Driver Circuit

Final Shutter Driver

f. AOMs

i. Theory An acousto-optic modulator (AOM) uses the acousto-optic effect to diffract and shift the frequency of light using RF. AOM’s generally are composed of some crystal, a transducer (usually with a PZT), and some absorbing material. When a control signal is applied to the AOM, an electrical oscillation causes the PZT to vibrate back and forth. These vibrations create sound waves which enter the crystalline material. This vibration compresses and expands the crystalline structure, changing the index of refraction of the material. It is this change that causes the diffraction and frequency shifting effects. When incident light enters the vibrating crystal it is diffracted based on the wavelength of light, and the wavelength of the sound vibrations.

2��� sin � = �������

� = sin���������

2���

Where m is the diffraction order of the light. As the light is diffracted, it is also shifted in frequency. This shift is what’s used to red-detune the ECDL output to match the doppler shifted atomic transitions. The resulting frequency shift can be found using the diffraction

order and the sound wave frequency.

���� = ��� + ����

ii. Schematics

Inputs Effect FM IN 0 – 10V, Shifts Frequency VCC 28V Power

AM IN 0 – 1V, Modulates Amplitude LIGHT IN Input Aperture

Outputs Effect RF OUT Resulting RF Frequency

LIGHT OUT Output Aperture

3. Software Design

a. Labscript Controller i. Theory

Labscript as a whole is an open-source experiment control system for automating shot-based experiments and their analysis. Experiments are composed as Python code, which is used to produce low-level hardware instructions. They are queued up and executed on the hardware in real time, synchronized by a pseudoclock. Experiment parameters are manipulated graphically, and analysis routines are run as new data are acquired. It was developed by the Bose–Einstein condensate (BEC) research group at Monash University in Australia, for use in the Spinor BEC lab of Dr. Lincoln Turner and Dr. Russell Anderson, and the Dual Species BEC labs of Prof. Kristian Helmerson. I was trained in its use by one of the developers, Chris Billington, at the National Institute of Standards and Technology and University of Maryland Joint Quantum Institute. The Labscript suite is made up of multiple programs that work together to automate an experiment to cool atoms and record data from the experimental run. Every shot starts with an initial Hierarchical Data File (HDF) configuration file. Each program reads and writes to this file; setting up an experiment based on the data within, writing new data to it, and passing it on to the next program in the line. Additionally, the suite also has a python library called “labscript” which attempts to offer a standardized interface to translate commands to devices that may or may not share a standardized communication or timing protocol. This gives the advantage of allowing a user to not only interface devices in a field that lacks any real standardization, but also add in any custom device they desire when needed. An average experimental “shot” occurs as follows:

1. The Runmanager GUI takes experiment parameters and encodes it into a HDF file.

2. The python library labscript is called and translates experiment logic – such as device commands, logic, etc into hardware instructions. The parameters encoded in the HDF file from Runmanager are inserted into this experiment logic and the instructions are encoded into the HDF file.

3. BLACS now takes the HDF file and begins interfacing with the devices based on the instructions within.

4. If external software is required for certain actions, such as communicating with a camera, BIAS is called and sends device instructions to the relevant software.

5. BLACS initiates the experiment and works through the entire experiment script contained within the HDF file. Each instruction is triggered at specific timings provided by the pseudo-clock powered by an external clock source.

6. All measurements provided by the connected devices are then written to the HDF file. BLACS sends a done signal to Runmanager and passes the HDF file to Lyse for analysis.

7. Lyse then proceeds to do any analysis routines written by the user. The results are printed to the screen in some fashion – Plots, Images, Command Line Output, etc

8. If repeated closed loop shots are required, MISE now takes over and interprets Lyse analysis to adjust experimental parameters. MISE adjusts parameters as needed and sends them to Runmanager for a new shot.

9. All software returns to an idle state until Runmanager sends a command for the next shot.

For a more in depth explanation of Labscript please see the full paper on the development of the suite: Starkey, P. T. , Billington, C. J. , Johnstone, S. P. , Jasperse, M. , Helmerson, K. , Turner, L. D. & Anderson, R. P. (2013). A scripted control system for autonomous hardware-timed experiments. Review of Scientific Instruments, 84, 085111.

ii. Schematics

iii. Software Flow

iv. Timing Timing diagrams are to be determined.

4. Glossary

Red-Detuning Optical light is retarded in such a way that its frequency is reduced and its wavelength increases toward the Infrared spectrum.

EMF Electro-Motive Force. In this context refers to the reverse voltage generated by a coil as the energy stored in its magnetic field is dissipated in an attempt to maintain the steady state flux.

Some form of density, depending on the context of the problem.

Q The total amount of energy in Joules C The specific heat of the material. Collimating Lens A type of lens that focuses the waist of a laser beam in such a way to

minimize its divergence. Holographic Grating A type of diffraction grating with a sinusoidal structure to its face. Incoming

light is split into various orders of diffraction based on the angle of incidence. These orders are then reflected outwards based on the angle of the holographic face.

Piezo Stack, PZT A type of crystalline material which expands or contracts under the influence of an applied electric field. These allow extremely accurate displacements of anything attached to them.

Thermo-electric Cooler A semiconductor device which makes use of the thermoelectric effect to create a temperature gradient between its two faces to rapidly cool or heat a surface.

Zeroth Order The light that corresponds to direct transmission, or specular reflection in the case of a reflection or holographic grating, is called the zeroth order, and is denoted m = 0.

Diffraction Orders, m An integer value which describes the mode of propagation of the diffracted light. Higher orders relate to larger angles and lower intensities.

Laser Modes Laser Modes are self-consistent electric field distributions in waveguides, optical resonators, or in free space. For lasers this is generally the standing wave pattern that is established within a resonating cavity.

Linewidth The linewidth (or line width) of a laser, typically a single-frequency laser, is the width (typically the full width at half-maximum, FWHM) of its optical spectrum.

Doppler Effect The Doppler Shift is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.

Hyperfine Splitting In atomic physics, hyperfine structure refers to small shifts and splitting in the energy levels of atoms, molecules, and ions, due to interaction between the state of the nucleus and the state of the electron clouds.

Circular Polarization Circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electric field of the wave has a constant magnitude but its direction rotates with time at a steady rate in a plane perpendicular to the direction of the wave.

Linear Polarization Linear polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. As the name implies, the wave oscillates in a linear fashion along one axis.

PWM A Pulse Width Modulation (PWM) Signal is a method for generating an analog signal using a digital source. A PWM signal consists of two main components that define its behavior: a duty cycle and a frequency. The duty cycle describes the amount of time the signal is in an on state as a percentage of the total time it takes to complete one cycle. The frequency determines how fast the PWM completes a cycle, and therefore how fast it switches between high and low states. By cycling a digital signal off and on in this fashion, the output will appear to behave like a constant voltage analog signal when providing power to devices.

RF Radio Frequencies Diffraction In classical physics, the diffraction phenomenon is described as the

interference of waves according to the Huygens–Fresnel principle that treats each point in the wave front as a collection of individual spherical wavelets. These behaviors are exhibited when a wave encounters an obstacle that is comparable in size to its wavelength. Similar effects occur when a light wave travels through a medium with a varying refractive index, or when a sound wave travels through a medium with varying acoustic impedance.

Runmanager Runmanager is a graphical user interface (GUI) used to aid the compilation

of labscript experiment scripts into hardware instructions to be executed on the hardware. Experiment parameters can be adjusted in the GUI, and lists of parameters can be used to create sequences of experiments, and scan over complex parameter spaces.

BLACS BLACS provides an interface to control hardware. It has a manual mode, as well as coordinating the execution of buffered experiments.

BIAS BIAS is a camera control program. It interfaces with BLACS to take images during experiments, while allowing the user to update regions of interest and camera settings.

MISE MISE closes the control loop, using analysis results to influence the creation of new experiment shots, via a genetic algorithm.

LYSE LYSE is an analysis framework. It coordinates the running of python analysis scripts on experiment data as it becomes availiable, updating plots in real time.

5. Appendix These components are approximate models. Final models, connections, and specifications are bound to change as the project evolves.

a. Camera Thorlabs DCC1645C - USB 2.0 CMOS Camera, 1280 x 1024, Color Sensor Input: USB Output: USB Power: USB

b. AOM Power: 28V DC - BNC Input:

FM IN 0-10V – BNC

AM IN 0-1V – BNC

Input Aperture – FIBER COUPLE

Output:

RF OUT – BNC

Output Aperture – FIBER COUPLE

c. Shutter NMLaser LST400 Laser Shutter Input:

RED – 24V Waveform to Winding

BLACK – GND to Winding

VIOLET – 5V DC

BLUE – Sensor GPIO

YELLOW – Sensor TTL Out

ORANGE – Sensor TTL Out

d. Pineblaster Digilent Max32: Arduino-programmable PIC32 Microcontroller Board To save time and space, the following information is retrieved from Digilent and the board’s datasheet. Power: USB or External 7-15V DC Input/Output: The Max32 board provides 83 of the I/O pins from the PIC32 microcontroller to pins on the input/output connectors J3, J4, J5, J7, J8, J9, and J14. The PIC32 microcontroller can source or sink a maximum of 18mA on all digital I/O pins. However, to keep the output voltage within the specified voltage range (VOL 0.4V, VOH 2.4V) the pin current must be restricted to +7/-12mA. The maximum current that can be sourced or sunk across all I/O pins simultaneously is +/- 200mA. The maximum voltage that can be applied to any I/O pin is 5.5V. For more detailed specifications, refer to the PIC32MX5XX/6XX/7XX data sheet

available from www.microchip.com. Connectors J3, J8, J9, and J14 are 2×8 female pin header connectors that provide digital I/O signals. Connector J4 is a 1×8 female pin header that provides digital I/O signals as well as UART1-3 and I²C communication signals. J18 is a 1×2 female pin header next to LD1 and LD2 that provides additional connection to the I²C signals. Connectors J5 and J7 are 1×8 female pin headers that provide analog inputs as well as digital I/O signals. Connectors J6 and J15 are two-pin headers that provide power and ground to shield boards. J6 provides two pins connected to the VCC5V0 bus and J15 provides two pins connected to GND. Note that although J6, J8, J9 and J15 are shown as separate connectors on the schematic, a single 2×18 connector is loaded across all of them when the board is manufactured. On connectors J3 and J14, the outer row (closer to the board edge) of pins corresponds to the I/O connector pins on an Arduino Mega or Mega 2560 board. The inner row of pins provides access to the extra I/O signals provided by the PIC32 microcontroller. The Arduino system uses logical pin numbers to identify digital I/O pins on the connectors. The logical pin numbers for the I/O pins on the Max32 are 0 – 85 and are labeled in the silk screen on the board. The analog inputs on connectors J5 and J7 are also assigned digital pin numbers. Pins A0 – A7 on connector J5 are digital pins 54 – 61, and pins A8 – A15 on connector J5 are digital pins 62 – 69. Pin numbers 70 – 85 are on the inner rows of connectors J14 and J3.