timing - Arduino: better microsecond resolution than micros()?

The micros() documentation notes that the return value will always be a multiple of 4.

Is there any way to get a higher resolution microsecond click, preferably down to the 1 microsecond level?

Dropping down to the AVR level is acceptable.

Answer

Yes, depending your Arduino's basic clock rate. For example here are the counter-timer input frequencies and periods after pre-scaling, for an ATMega2560's counter-timer 2, and a basic clock rate of 16MHz. The timer has built in "prescaler" value options which determine frequency/period, shown in this table:

    TCCR2B bits 2-0    Prescaler    Freq [KHz], Period [usec] after prescale
          0x0          (TC stopped)      --         --
          0x1                1        16000.        0.0625
          0x2                8         2000.        0.500
          0x3               32          500.        2.000
          0x4               64          250.        4.000

          0x5              128          125.        8.000
          0x6              256           62.5      16.000
          0x7             1024           15.625    64.000

For better timing resolution, you use a value called TCNT2. There is build in counter that goes from 0 to 255 because the timer is 8 bit. When the counter reaches the value assigned by TCNT2 it triggers an interrupt. This interrupt is called TIMER2_OVF_vect.

given this information, the resulting interrupt rate would be: 16MHz / (prescaler * (255 - TCNT2))

You could get the timer to run at the full 16MHz (62.5nSec) though that's way faster than you need; 2MHz with an initial count of (255-2) would give you 1MHz interrupt rate. Divide that by 2 in your ISR:

extern uint32_t MicroSecClock = 0;

ISR(TIMER2_OVF_vect) {// this is a built in function that gets called when the timer gets to the overflow counter number

  static uint_8 count;            // interrupt counter

  if( (++count & 0x01) == 0 )     // bump the interrupt counter
    ++MicroSecClock;              // & count uSec every other time.

  digitalWrite(53,toggle);// pin 53 is arbitrary
  TCNT2 = 253;                    // this tells the timer when to trigger the interrupt. when the counter gets to 253 out of 255(because the timer is 8 bit) the timmer will trigger an interrupt
  TIFR2 = 0x00;                   // clear timer overflow flag
};

The data sheet for your MCU is the basic resource; this article will give you (and gave me!) a good head-start.