Make sure whatever or however you sort this out is down in writing and that both you and your boss sign it.
I spent more than 17 years travelling the world with various different companies and I can tell you now that unless it is down in black and white on a pieve of paper you both signed and have a copy of, they WILL always argue about who owes who what.
Some of the companies I have worked for have paid from the minute I left my house to the minute I arrived at the destination hotel/factory. Others have paid from the time I arrived at the airport to the time I arrived at the destination hotel/factory.
I personally have NEVER agreed to fund expenses out of my own pocket to be reimbursed later. I've known people that have done this and found that they have always had to fight for their money.
I find that the per deim system is becoming more popular recently (even more so with American based employers), but personally prefer a company credit card and a good set of guidelines as to what is/is not an acceptable expense.
Some companies are more generous than others (someday I'll tell the story about the Rio Carnival trip I was paid to go on) and some like to leave a little "grey" area that can be manipulated, trust me - the grey area will always be viewed in the companies favor by an accountant.
It doesn't hurt to remind your boss what you are sacrificing - eating at your favorite home restaurant, socialising with friends and family, trips to the movies, etc. Remind your boss that if you are not required to work weekends whilst travelling then a little more money may be required to stop boredom and depression setting in.
Just make sure that both you and your boss are clear on what is expected from both of you, and make sure the trip is enjoyable (there's nothing worse than worrying about money everyday you are away from home).
Oh, and by the way enjoy Japan, it's been a while since I've been but I love the place and the people, and if you've never travelled to an Asian country before be ready for some shocks as the culture is VERY different from life here in the states.
Looking forward to hearing some stories when you make it back
Just my opinion.
Mart B