From the documentation of this library:

The library use no interupts of the hardware timers and works with the micros() / millis() function.

This library implements timers in software by polling the micros() and millis() functions. It requires the update() method to be called in loop().

So the start of loop() should be:

void loop()
{
    tickerObject.update();

    if(s == true)

I'm trying to use a Ticker.h to sample an analog input consistently at a frequency of 10khz

It is worth a go but this is a software based solution that is prone to jitter depending on how often the event loop can be called.

I think you might struggle to get a microsecond delay that is both accurate and non-blocking with the ESP8266.

According to the NodeMCU documentation:

If you look at the app/modules/tmr.c code for this function, then you will see that it executes a low level ets_delay_us(delay). This function isn't part of the NodeMCU code or the SDK; it's actually part of the xtensa-lx106 boot ROM, and is a simple timing loop which polls against the internal CPU clock. It does this with interrupts disabled, because if they are enabled then there is no guarantee that the delay will be as requested.

tmr.delay() is really intended to be used where you need to have more precise timing control on an external hardware I/O (e.g. lifting a GPIO pin high for 20 μSec). It will achieve no functional purpose in pretty much every other usecase, as any other system code-based activity will be blocked from execution; at worst it will break your application and create hard-to-diagnose timeout errors.

It seems that interrupts have to be disabled in this case simply because if an interrupt did occur mid-delay with a short interval (on the order of a few microseconds), the interrupt handler would take up far more time than the whole delay was supposed to be.

Let's say you wanted a timer for 20 microseconds, and an interrupt occurred at about 10 μs. If the handler takes more than 10 μs, you will have already passed the 20 μs delay that you intended.

So, we can rule out tmr.delay() if you do need interrupts working.

I did a bit more digging, and apparently the ESP8266 does support microsecond timers through ets_timer_arm_new() where the last parameter is zero. NodeMCU, however, sets this value to 1 which uses the millisecond precision. This post seems to support that idea:

If you need to get the interval between two gpio interrupt, use the system api system_get_time() to calculate the relative time.(us) If you want to use a os_timer api to arrange a us timer event, use system_timer_reinit at the beginning of user_init and call os_timer_arm_us.

If you're willing to try editing and rebuilding the firmware, it might be worth a shot. Although, there was a feature request for this, which was declined as:

So I tested nanosecond timers, and cannot establish intervals less than 1000us (with compiled and stripped code and in 160MHz CPU mode I got something like 800us). Is this a case to provide new (mostly unusable) functionality?
- djphoenix

Not feasible ATM -> closing.
- marcelstoer